The 35-year-old was named Man Of The Match after the performance at the Stade de France, which saw Ireland score three tries during a hard-fought tournament decider.
An emotional O'Driscoll, who kissed the trophy as he ended his 15-year international career, said: "It feels great to be a two-time Six Nations winner. It's great to finish on a high in my last game in this magnificent jersey.
"When I do hang it up on the hook inside, it'll be with very fond memories.
"I'm absolutely delighted. There's a huge Irish contingent here. I'm glad we gave them something to shout about.
"It was last-leg stuff and I know now why I'm packing it in because 80 minutes is a long bloody time at international level, particularly with guys like Mathieu Bastereaud running at you - it's no fun," O'Driscoll added.
Johnny Sexton ran in two tries, missed five points with the boot and was knocked out cold trying to tackle wrecking ball centre Mathieu Bastareaud.
Ireland rebuffed a late French onslaught to claim their first Six Nations title since 2009, with wing Andrew Trimble also on the scoresheet after one of the best performances of his international career.
Ireland captain Paul O'Connell was delighted his team could give O'Driscoll the perfect send-off.
"To be part of the team that laid the platform for him to have a great finish to his career is great for everyone involved," he said after leading Ireland to just a second win in 42 years in Paris.
It's fantastic for Ireland, for the people back home but also for Brian and his family.
Captain Paul O’Connell
At the start of the game, Ireland were forced to weather a hefty first-quarter storm.
Maxime Machenaud slotted two penalty goals to nudge France into the early lead, Bastareaud blasting through the visiting backline on three occasions.
Chris Henry's cute offload outfoxed the home defence after smart build-up play, and Sexton caught sight of the half-gap to cut back inside and over the whitewash.
The former Leinster playmaker scuffed the conversion though, a straightforward effort he should have buried, leaving Ireland trailing by one point.
Ireland quickly doubled their try count thanks to Ulster wing Trimble, but they still trailed 13-12 at the break, after Brice Dulin crossed for the hosts.
Sexton started the second-half in the manner he finished the first, his risky chip easily dealt with by Gael Fickou, setting France away on a trademark counter-attack.
Ireland and Sexton had two rescuers to thank for avoiding serious censure: first Rob Kearney swept up Huget's chip in behind then O'Connell won a vital ruck turnover penalty.
Rob Kearney again cleaned up the mess, latching onto a deft boot through the line from the French to clear, after Mike Ross' knock-on.
Sexton quickly scotched those errors and the five missed points from his and Ireland's minds though, racing in for his second and his side's third try of the night.
When Huget failed to hold Bastareaud's pass, it was Ireland launching the counter through Rob Kearney.
Andrew Trimble cut away down the right, feeding O'Driscoll, who had the presence of mind to recycle deep in the France 22.
O'Connell carried on, and Murray sent Sexton under the posts.
In one swoop, suddenly Ireland were once again sure of themselves, winning a penalty for Sexton to shoot at goal.
This time there was to be no mistake, the 28-year-old firing home with assurance renewed thanks to try number two, to put Ireland 22-13 to the good.
France battered Ireland's final defences time and again as the hosts launched a sustained assault after a penalty line-out in the 22.
O'Connell conceded a penalty on the try line, and France again punted for the line-out rather than shoot at goal.
Bastareaud thundered into midfield, Louis Picamoles drove to the right-hand post, and hooker Dimitri Szarzewski bundled in.
Referee Steve Walsh awarded the try, but replays suggested the Racing Metro hooker fumbled in the act of scoring.
Machenaud landed the conversion, to cut Ireland's lead to just two points.
Sexton's mixed night took another turn when he was knocked out cold trying to fell Bastareaud.
The Toulon battering ram put Sexton in the recovery position before Ireland's medical team carried him from the field by stretcher.
So Ian Madigan was pitched into his first Six Nations action of the season, at the crucial moment.
Heavyweight replacements Alexandre Flanquart and Sebastien Vahaamahina beefed up France's scrum, forcing a penalty as Ireland were rocketed backwards.
Jean-Marc Doussain had the chance to steal the lead from the tee, but could only shoot wide.
Damien Chouly thought he had stolen the game when he nipped into the right corner, but Vincent Debaty's pass was ruled forward and the last-minute try was disallowed.
France stole Ireland's scrum, only for the visitors to win a turnover at the ruck, and spark jubilant celebrations at the final whistle.