The 22-year-old's former club IFK Norrkoping said he had a heart defect.
DC United's general manager Dave Kasper said: "The MLS cardiology consultant and a heart specialist at MedStar Georgetown University Hospital determined he could resume playing.
"Kamara will undergo testing at the end of each season."
The Sierra Leone international's move to DC United comes at a time when two Cameroonian players Patrick Ekeng and Jeanine Christelle Djomnang died of suspected heart problems.
Kasper added: "The player had a potential cardiac issue that could have eliminated him from playing. He was evaluated and found this was not the case.
"We went through proper medical testing and approvals from two top cardiology specialists.
"Certainly we went through a rigorous process, but once they cleared him to play, it gave us peace of mind."
A transfer fee has not been paid for Kamara but Norrköping will be compensated if the player meets performance incentives or if he is sold in the future.
He was originally examined as part of a Uefa requirement because IFK Norrkoping are due to take part in the qualifiers for next season's Champions League.
'He is a strong guy'
Experts from both Uefa and Fifa had advised Kamara against continuing playing football.
This initially forced Norrkoping to remove Kamara from their 2016 season squad to stop him from playing more matches.
Kamara, who scored six goals to help Norrköping win the 2015 Swedish league, is delighted that his career can resume.
"He is so happy and excited to be able to play again," Kamara's local agent Chernor Musa Jalloh told BBC Sport.
"Physically and mentally he is prepared and he knows everything as he is a strong guy.
"He went through a difficult path and thanks to everyone who supported him."
Sierra Leonean striker Alhaji Kamara has been given medical clearance to resume his career after heart tests and has signed for DC United in MLS.