The 23-year-old has joined Thomas Frank’s side for a £13.5m fee and is the club’s second summer signing following the arrival of Nigeria international midfielder Frank Onyeka from Danish side Midtjylland earlier this week.
Ajer had been at Celtic since 2016 and had one year remaining on his contract.
The former IK Start defender won three league titles, three league cups and three Scottish cups in his time with the Bhoys.
Brentford head coach Thomas Frank said: "We wanted to get another central defender in, and Kris was our first choice. We think he fits the position-specific profile perfectly, especially on the ball.
"Kris is very composed and can find the right passes between the lines. His level when bringing the ball forward is very high.
"As a defender he has the physicality that you need, and he won his duels when he played in the Scottish league. He can help us in both boxes, with his strength in the air.
"He is a player at a good age, and we think he come straight in and be ready to perform in the Premier League. But he also fits the way we want to recruit players and work with them.
"He can develop as a player and both Brentford FC and Kris can move to a higher level in the coming years."
Ajer has won 23 caps for the Norway national team.
Brentford start their first season in the Premier League with a home game against Arsenal on August 13.
