On searching Google - Brahmotsav is an annual festival of nine days. Although it is celebrated on various days in different temples, but in Tirumalaa Lord Venkateshwar Temple (Tirupati Jee) it is celebrated in the Tamil month of Purattasee - in the months of September and October (between 18 September and 18 October). It starts on the first day of Aashwin Nava Raatri there. It is celebrated in other Vishnu temples also but differs on dates temple by temple. This festival is related to Vishnu and His Avataar. Brahmotsav in Tirumalaa is also conducted at three other times of the year, namely: Kaishikaa Ekaadashee (also known as, Raakshas Brahmotsav), Mukkoti Dwaadashee (also known as, Daiv Brahmotsav) and Rath Saptamee (also known as, Aarsh Brahmotsavam). Besides, these 4 Brahmotsav in a year, it is also celebrated as a Shraaddhotsav as desired by devotees. It is stated that in the year 1551 AD, as many as 11 Brahmotsav took place.

Popular stories seek its origin to Brahmaa Jee who first worshipped Baalaa Jee as a way to give thanks to Him at Tirupati on the banks of holy pond Pushkarinee. Another legend says that once Indra killed a Brahm Raakshas (Braahman with demonic characteristics), so he was attached Brahm Hatyaa sin. To clear him from this, Brahmaa Jee conducted a ceremony in which Indra kept Shree Man Naaraayan on his head, and took a special ritual bath (Avabreet Snaan) - and this was the first Brahmotsav. So because of immense cleansing power, this Utsav is periodically celebrated all over the year to wash away all the sins. It is common belief that every Brahmotsav is witnessed  by Brahmaa Jee.

The earliest inscribed record of Brahmotsav at the Thirumalaa Temple is 650 AD. References to Brahmotsav can be found in Varaah Puraanam (ch 18) and Bhavishyottar Puraanam (ch 24).

How Brahmotsav Is Celebrated
On the first day of its celebration, the rite of Ankuraarpan (sowing the seeds of nine grains in soil paced in earthen pots to signify fertility, prosperity and abundance) is performed along with a festival of Shree Vishwaksen. Dhwajaarohan - the hoisting of the Gaud marked flag on the Dhwaj Stambh is done. This signifies the starting of the Brahm Utsav. It is believed that after this Garud Jee goes to Vishnu Lok and and invites Vishnu Jee and other Devtaa to attend the function. Kankan Dhaaran, wearing the wristband, is done.

During the nine days, religious activities include daily Hom, processions of the Utsav Moorti on different Vaahan (chariots), adorning the Moorti with different jewelry every evening. The concluding day is the birth start of Baalaa Jee day. This day is celebrated in a grand way. In Tirupati, the Sudarshan Chakra is bathed in Pushkarinee River. In Auroraa, a pries takes a holy bath near the Dhwaj Stambh. Then the Chakra is put on a high platform, so that devotees can walk under it and be blessed with its dripping water. The festival concludes again with the Dhwajaarohan (lowering the flag) and with this the priest sends all Devtaa back to their Lok.

Everyday of the Brahm Utsav is feast to eyes. The nine Vaahan are -
(1) Peddaa Shesh Vaahan (of 7 heads),
(2) Chinna Shesh Vaahan (of 5 heads),
(3-morning) Sinh Vaahan,
(3-evening) Muthyaalaa Pallakee (The Moorti is taken with His consorts Shree Devee and Bhoo Devee in a palanquin decorated with pearls),
(4-morning) Kalp Vriksh Vaahan,
(4-evening) Sarv Bhoopaal Vaahan,
(5-morning) Mohinee Avataar - procession as Mohinee Avataar in ivory palanquin,
(5-evening) Garud Avataar - Lord seated on Garud, with chanting Mantra from Taitteerya Sanhitaa related to Garud, witnessed even by the Chief Minister of Aandhra Pradesh
(6-morning) Hanumant Vaahan
(6-evening) Gaj Vaahan or Swarn Rathotsav - seated on elephant
(7-morning) Soorya Prabhaa Vaahan - with Soorya Dev
(7-evening) Chandra Vaahan - with Moon
(8-morning) Rathotsav - on a fully decorated chariot along with His consorts, goes around the village pulled by thousands of devotees, and greeted by thousands of devotees on the way
(8-evening) Ashwa Vaahan - for Hayagreev Avataar and Kalki Avataar
(9-morning) Chakra Snaan
(9-evening) - Dhwajaarohan.

Brahmotsav
I found the following description in "US Brahmins" Group appeared on March 13, 2011.

Once, Dharmvarmaa, Rishis and all devotees got together and wanted to have your Darshan in Srirangam. Dharmvarma requested Vibheeshan permission to conduct Brahmotsav for you in Srirang. The Brahmotsav was celebrated in all its divine glory. Thereafter Vibheeshan tried to lift you along with his Vimaan (to take to Srilankaa). He could not do so. This was your will. Accordingly, on Panguni, Rohinee noon during Abhijeet Nakshatra, you were installed in Srirangam.
- (108 / 52 - 54)(from Sri R V Swamin’s Divya Desa Manimala)

This Brahmotsav is the only ancient Utsav celebrated by Brahmaa in Brahm Lok and by all the Soorya Vanshee kings including Shree Raam in Ayodhyaa. This is also the Utsav celebrated by Dharmvarma and Vibheeshan together in Srirangam. This is also the first Utsav celebrated after Sri Ranganaath was installed in Srirangam. Rohinee is the birth star of Sri Rangnaath. It is also the birth star of Krishn. Because of the great liking the Lord has for Rohinee, the Brahmotsav in Srirangam begins in Rohinee.

It is said that in Brahm Lok when Brahmaa and other Devtaa were thinking about the ways for the spiritual uplift of human beings, Lord Vishnu along with His Pranava Swaroop Vimaan and Dwaarapaal descended on Thiru Parkadal. If He stays in Thiru parkadal, how to uplift the human race? So, the Lord selected Srirangam as His abode. All this is fine. But without Thayar’s Kataaksham how can the humans be uplifted?

The legend is that, according to Thiru Aanaika Puranam (by Sri Kachiappar), Thayar had already come down to Srirangam as Sri Ranagnaayakee. This is perhaps one of the reasons Lord also came to Srirangam! The sacred Utsav begins during Rohinee. It is completed on Panguni Uthram, the birthday of Thayar. The Divya Dampatti (Divine couple) vowed to uplift the human race from here.

Sri Raamaanuj understood this clearly. He realized this was the time for Sharanaagati. Accordingly, he composed Gadya Trayam - Sriranga Gadyam, Sharanaagati Gadyam and Vaikunth Gadyam. Through these gems, he showed us the way to attain Moksh.

Aadi Brahmotsav Thirunal
The holy festival of Aadi Brahmotsav starts on 03/11/2011 on the First day of Masi 27. There is an interesting background for the second day. There was once an aged woman who was a great devotee of Sri Rangnaath. She had a grandson by name Rangan. They lived in Jeeyarpuram, a small village on the banks of Kaveri. In those days Kaaveree never went dry. Once Rangan went to Kaaveree to bathe. The river took him away and left him on the banks near Ammaa Mandapam at Srirangam. Rangan had Lord's Darshan. He also prayed for his grandmother. Here his grandmother was searching for him then Rangnaath appeared before her in the form of her grandson. The woman took him home and fed him. By this time, the real grandson returned home and Lord Rangnaath disappeared. Every year on this day Sri Rangnaath arrives in Jeeyarpuram.