The alleged incident happened following Doncaster's 3-1 defeat at The Liberty Stadium on 21 February.
Wellens was asked to respond to the charge and he was cleared of the allegations at an FA hearing and will face no further action.
Rovers boss Sean O'Driscoll said: "We are pleased that this case as now been resolved and that we had a fair hearing by the FA.
"We would have abided by any decision that the FA had come to but now we can get on with the football."
The alleged incident - described as "unacceptable" by Swans boss Roberto Martinez - was said to have happened while Rovers' James Coppinger was being treated for concussion.
After the alleged incident, Britton said: "It's the first time it has happened to me and hopefully the last because it's a disgusting thing.
"I would rather him have punched me than spit in my face, it's a bit of a cowardly thing to do."
But Wellens pleaded his innocence and insisted: "I did not spit in his face but I was clearing my throat and did not aim anything his way."
The FA had said the alleged incident was not caught on camera or spotted by match referee Scott Mathieson but Swansea made the complaint and sent a copy of the match DVD to the authorities.
The FA's compliance unit talked to both sides before making their decision.
Before the hearing, Rovers chief executive Dave Morris said the club was "surprised and shocked" by the charge.
"It is only backed by the testimony of Leon Britton with little or no supporting evidence," he said.