A full-season deal with the Italian squad follows the Australian's cameo at the post-season test in Abu Dhabi late last year.
He was 10th fastest on the first of the three days despite having no experience in F2.
Williams' promotion to F2 follows two seasons in Formula 3 with Jenzer Motorsport, the 2021 campaign yielding his first podium and 19th place in the points.
"I'm extremely proud that a team so incredibly competitive and professional like Trident Motorsport welcomed me to its line-up," said Williams.
"I worked very well with the team's staff in the last few months and in the FIA Formula 2 Championship post-season test.
"I have a unique chance in front of me and I will give my 100 percent to use my full potential and show my skills on track. I'm really delighted that Trident Motorsport welcomed me to the team so warmly and believed in me."
Trident team manager Giacomo Ricci said Williams impressed the squad during the Abu Dhabi test.
"We are delighted to welcome Calan Williams to our line-up," he said.
"He did very well in the post-season FIA Formula 2 test held at Yas Marina last December. Calan quickly adapted to a car of a superior series and set competitive marks in terms of overall performance and race simulations.
"Our technical staff was really impressed by his performance, but he also shined in terms of work ethics and commitment that he poured in to be always competitive, day in, day out.
"These aspects quickly created a strong bond between him and the team, so Trident Motorsport is proud to have secured such a strong driver to face a really demanding series like the FIA Formula 2 Championship."
Testing for the 2022 F2 season kicks off in Bahrain on 2 March.
