Rodgers guided Celtic to the league title and the Scottish League Cup in his debut season after succeeding Ronny Deila.
The former Liverpool manager signed a 12-month rolling contracting in May, 2016, but has committed his future to Celtic until 2021.
Upon extending his stay at the Glasgow club, Rodgers said: "It just felt right. Myself, Peter and the board been talking for a little while and it felt the right thing to do.
"I find it hard to find the words to express my feelings."
Read the full article on eurosport.co.uk: Celtic manager Brendan Rodgers signs new four-year contract