No other nominations were received for the BCCI's secretary's post. The AGM was chaired by BCCI President Anurag Thakur.
Shirke became the secretary in July after Thakur was elevated to the president's post, vacated by Shashank Manohar who quit BCCI to become the International Cricket Council (ICC) chairman. He is also chief of the Maharashtra Cricket Association (MCA).
A new five-member selection panel was formed, headed by Prasad (South Zone), which also included former off-spinner Sarandeep Singh (North Zone), ex-batsmen Gagan Khoda (Central Zone), Devang Gandhi (East Zone) and Jatin Paranjpe (West Zone).
Gandhi, Paranjpe and Singh were the new additions to the panel. Prasad, who was part of the earlier selection panel, replaced Sandeep Patil as its chairman.
He played six Tests and 17 One-dayers for India between 1998 and 2000, having made his international debut against Bangladesh in an ODI in 1998.
He played his first Test against New Zealand in 1999. In 2000, however, he was dropped from India's Test squad and did not play international cricket again.
He featured in 96 first-class matches, amassing 4,021 runs at an average of 27.73 and claimed 266 dismissals. He also scored 1,719 runs in 88 List A games.
The 41-year-old was appointed the Andhra Pradesh captain for the 2007-08 Ranji Trophy season.
He announced his retirement from the game in 2008 and later served as Andhra Cricket Association's director for six years.
The Guntur-born became a national selector in 2015. He has also served as selector for the India U-19 team.
"It's undoubtedly a great honour. I have a clear-cut vision about how we are heading to the 2019 World Cup," Prasad was quoted as saying by espncricinfo.com after his appointment.
"I always have kept notes about what I want to do for the 2017 Champions Trophy, for the 2019 World Cup. There is a lot of planning. The best thing is we have watched as many domestic matches as possible."
"We have done tours to Zimbabwe, Australia only at the end of the season. Because we have watched so much domestic cricket last year we have a succession chart and jotted down names for three different formats."
Former India pacer, Venkatesh Prasad was retained as the chairman of the junior national team's selection committee. Ashish Kapoor and Amit Sharma were added to the junior selection committee.
It was also decided that Thakur will continue to remain BCCI representative at the ICC and the Asian Cricket Council.
Mumbai Cricket Association vice-president Ashish Shelar was appointed marketing committee chief.
BCCI held its AGM for 2016-17 despite the Justice Lodha committee's recommendations which stated the board not conduct any new business.
The Lodha committee also recommended a three-strong panel with all members having Test experience.
The new selection committee has a combined international experience of 13 Tests and 31 One-Dayers.
But two of its selectors, Gagan Khoda, who was retained in the committee, and Paranjpe have not played Tests.
