Britton had a short spell with Sheffield United in the 2010-11 campaign, but aside from that the midfielder and Monk have been team-mates for around a decade.
Monk was charged with the task of replacing Michael Laudrup earlier this month after the Premier League club parted company with the Dane.
The Englishman told the club's official website: "It's always going to be strange at first because one minute you're team-mates and the next you're calling him gaffer.
"I guess it was even stranger for me because I've roomed with him on away trips.
"He's been here as a leader on the pitch for years, and now he's the leader off it so it has felt like a natural transition for him.
"He has a great understanding of the game and we've seen that with his tactical analysis already.
"The board and players know him well, he's well respected and I think the fans have really got behind him too."
