Haas, currently seventh in the 10-team constructor standings, said Toyota would provide "design, technical and manufacturing services".
Magnussen has driven 135 races for Haas, and driven for them in seven different seasons.
The longest season in Formula 1 history starts this weekend with the Bahrain Grand Prix
Mick Schumacher will not be taking part in Sunday's Saudi Arabian Grand Prix after a horror crash in qualifying at Jeddah's high-speed street circuit.
Formula One: Kevin Magnussen has signed a multi-year contract agreement with Haas and will replace Nikita Mazepin.
Recently sacked by Haas, Russian driver Nikita Mazepin will be creating a foundation to provide help to sports persons barred from competing due to political reasons.
Russian driver Nikita Mazepin said he was "very disappointed" at being dropped by Formula One team Haas on Saturday due to Russia's invasion of Ukraine and hinted he might take action over "this unilateral step".
Formula One team Haas on Saturday announced they have dropped Russian driver Nikita Mazepin and terminated their contract with title sponsor Uralkali due to Russia's invasion of Ukraine
Formula 1: Max Verstappen's title triumph garnered mixed reactions from the F1 fraternity as several former and current drivers expressed their views after the conclusion of the race.
Haas driver Nikita Mazepin has tested positive for COVID-19 and will not take part in Sunday's season-ending Grand Prix in Abu Dhabi, his team said.
22-year-old Mick Schumacher, son of seven-time former world champion Michael Schumacher, will continue to race for the Haas team in the 2022 Formula One season, it was confirmed on Thursday.
Mick Schumacher said he is "very happy" to carry his family name back into Formula One.
Mick Schumacher, the Formula One-bound son of seven-time world champion Michael Schumacher, clinched the Formula Two drivers' championship title on Sunday.
The International Automobile Federation (FIA) said it had "initiated a detailed analysis of Romain Grosjean's accident at the 2020 Bahrain Grand Prix".
Haas announced that Mick Schumacher, son of legendary driver Michael Schumacher, will drive in Formula One for the first time next season.
Seven-time world champion Michael Schumacher's son Mick will drive in Formula One for the first time with Haas next season.
Romain Grosjean, 34, trapped in his cockpit, flew under the barrier as it gave way and as his car burst into flames, splitting in two on impact.
Formula One announced that all 10 teams have agreed to the new Concorde Agreement.