Healy was banned for three weeks for stamping on fellow Lions front row contender Dan Cole in the defeat to England in Dublin on February 10.
The implementation of that suspension was delayed for a week, however, to ensure he would miss the home tie with the French as well as last Sunday's trip to Scotland.
Healy accepted the level of suspension but appealed against the timing.
The three-man appeal committee met in Glasgow yesterday and subsequently decided that the ban should have begun immediately after the game against England.
That means Healy is now free to play from March 3 and will be available for the Round 4 clash with winless France at the Aviva Stadium a week on Saturday.
The news is a major boost for Ireland, who have now lost their last two Championship matches and are without a number of frontline stars.
Fly-half Jonathan Sexton remains a doubt after missing the Scotland game, wing Simon Zebo is out for the remainder of the Championship with a broken foot, and hooker Richardt Strauss won't play any part either as a result of ankle ligament damage.
Flanker Chris Henry is another to miss what's left of the tournament after a knee operation presented him with a likely four-week spell on the sidelines and veteran centre Gordon D'Arcy will remain in a moon boot until the middle of next week following a stress injury in his foot.
Lock Donnacha Ryan and wing Craig Gilroy had MRI scans on shoulder and groin damage respectively after the loss at Murrayfield and, while the scans didn't show any serious damage, the pair will undergo a period of rehabilitation and are uncertain of featuring against the French.
Ryan's second row partner against the Welsh and English, Mike McCarthy, still has to prove that he has recovered from the knee injury that prevented him from playing in Edinburgh, while the likes of Lions trio Paul O'Connell, Stephen Ferris and Tommy Bowe haven't featured at all in 2013.