The deal carries an average annual value of $2.75 million.
The two parties were slated to have an arbitration hearing on July 29.
The 26-year-old from the Czech Republic had a breakout 2018-19 campaign, making a career-high 42 starts as part of a tandem with Mike Smith. He also posted personal-bests in save percentage (.911) and goals-against average (2.61).
Calgary also signed former Edmonton Oilers netminder Cam Talbot to a one-year, $2.75-million contract on July 1, while the Oilers grabbed Smith in free agency on a one-year, $2-million deal.
The six-foot-three, 206-pound Rittich has compiled a .909 save percentage and 2.70 GAA across three years and 67 games with the Flames.
He previously spent two years with BK Mlada Boleslav in the Czech Extraliga.