The former England cricket captain, 45, appeared with facial injuries in public for the first time in September, nine months after he was taken to hospital after he was hurt while filming the BBC motoring show at its test track at Dunsfold Aerodrome last December.
Both Flintoff and the BBC are "satisfied" with the agreement, according to the Sun's Saturday front page, which claimed the settlement is worth nine million pounds ($A17.3 million).
"BBC Studios has reached an agreement with Freddie that we believe supports his continued rehabilitation, return to work and future plans," A BBC Studios spokesperson said.
"We have sincerely apologised to Freddie and will continue to support him with his recovery."
The BBC said in March that it would be inappropriate to resume making the series at that time following an internal investigation into what happened.
It is understood that the decisions on future episodes of Top Gear will be made "in due course in conjunction with BBC Content".
Series 34 was halted following the crash.
Flintoff began presenting Top Gear in 2019, and also appeared on Sky's A League Of Their Own and won the first series of the Australian version of I'm A Celebrity... Get Me Out of Here!
His other shows with the BBC include Andrew Flintoff's Field Of Dreams, where he embarked on a mission to find cricketing talent in his home town of Preston.
In September, Flintoff joined the coaching staff of England's cricket team in a temporary, unofficial and unpaid capacity.
Representatives for Flintoff have been asked for comment.
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