The Scottish League One bottom club acted quickly after sacking Jimmy Boyle on Sunday following a 2-0 home defeat by Forfar 24 hours earlier.
Former Rangers and Dundee United defender Bollan will take charge after Saturday's game against Ayr with his first two games both coming at Ibrox in the Scottish Cup and league.
Airdrie chairman Jim Ballantyne told the club's official website: "Sunday was a sad day with the departure of Jimmy Boyle but the board felt that it was time for a change.
"We have been overwhelmed with applications from home and abroad and the standard was extremely high, which reflects the current difficulties facing Scottish football.
"The board agreed a list of priorities and objectives and after a lot of research it was clear that Gary Bollan was the preferred candidate."