Drivers Romain Grosjean and Kevin Magnussen will both leave Haas at the end of the 2020 season.
France's Grosjean, 34, has been with Haas since the team entered Formula 1 in 2016 while Dane Magnussen, 28, moved from Renault in 2017.
Grosjean is 18th in the drivers' championship with two points and Magnussen is 19th having scored one.
It means Haas, currently ninth in the constructors' standings, will have an entirely new driver line-up for 2021.
Grosjean said team owner Gene Haas told him the move was for financial reasons.
"I knew probably one of us would go out because the financial situation with Covid has made life difficult for companies around the world," Grosjean said.
"But when I spoke to Gene, he said: 'For financial reasons, I need both of you out.'"
Grosjean has scored 110 points in 92 races for Haas - a fourth-placed finish at the 2018 Austrian Grand Prix his best result.
Magnussen has raced 73 times for the team, winning 96 points.
In 2018 the team achieved their best finish in the constructors' championship by coming fifth.
Magnussen said he had had a "great time" with the team and will announce plans for the future "in due course".
Grosjean did not give details on his future plans but wished the team the best for the future.
"I have learned a lot, improved to be a better driver as well as a better man, "said Grosjean, whose first points of the season came at the Eifel Grand Prix on 11 October.
Team principal Guenther Steiner said: "I want to extend my thanks to both Romain and Kevin for their hard work and commitment to Haas F1 team over the past few seasons. We have a lot of good memories together."
Analysis - Mick Schumacher to come in?
BBC Sport chief F1 writer Andrew Benson
The decision by Haas to move on Grosjean and Magnussen reflects the team's shifting priorities heading into 2021.
Resources are tight at the team owned by billionaire machine-tools magnate Gene Haas and it is likely that at least one of the drivers Haas brings in next year will have financial backing.
Grosjean and Magnussen have been evenly matched through their careers together at the US-based team.
But both take salaries. F1 is introducing a major new rules package for the 2022 season. All teams hope the new, radically different cars will provide a competitive reset, and Haas needs resources to ensure it is as well prepared for that season as possible.
It is unclear as yet who will take the seats, but Russian Formula 2 driver Nikita Mazepin has been strongly linked to the team.
Mazepin's father Dimitry is a billionaire who owns a major chemicals company. He has backed his son's career and has been looking for a way into F1 for some time.
Mick Schumacher, son of seven-time champion Michael, has also been linked to a drive at Haas.
He is part of the Ferrari driver academy and Haas have close links with the Italian team, buying as many parts from them as the rules allow.
Schumacher has also been linked with Alfa Romeo, another Ferrari satellite, and his destination may depend on whether Ferrari decide Antonio Giovinazzi, another of their proteges, has done enough to secure his seat at Alfa for a third season.
- New drama - Roadkill: Can a government minister outrun the secrets of his past?
- Bringing Football Back: Behind the scenes of a club reborn