Breaking his claycourt jinx against the Swiss, second seed Murray also becomes the first Briton to contest the Roland Garros crown since the 1930s -- a landmark he did not think he would achieve.
"I am extremely proud. I never expected to reach a final here," he said courtside after a 6-4 6-2 4-6 6-2 victory that cemented his growing reputation on a surface he once mistrusted.
"I knew today if I wanted to win I would have to play one of my best claycourt matches. I played one of my best matches today."
Murray bested Djokovic in May's Italian Open final, their most recent encounter on clay.
But the Briton is likely to have to up his game further to repeat the performance on Sunday against a man who looked all but unplayable in crushing Austrian tyro Dominic Thiem 6-2 6-1 6-4 a stone's throw away on Court Suzanne Lenglen.
Looking re-energised after a rest day that the pair on the other side of the draw missed out on, both Murray and Wawrinka started brightly, the Scot pacing in monochrome while the Swiss lit up a dull Philippe Chatrier showcourt in fluorescent yellow.
Murray came close to losing his very first service game, which he took after five deuces. But he then broke his third-seeded opponent and consolidated with a pinpoint lob to lead 3-1, winning the set in an epic 10th game in which Wawrinka held three break points.
TAKING CONTROL
With Wawrinka's trademark booming backhand slightly misfiring, Murray, who held a winning 8-7 record against the Swiss but had lost their three contests on clay, then took a firmer grip on the match.
The Scot moved higher up the court as he began to anticipate his opponent's groundstrokes, breaking to lead 2-1 and then again for 4-1, sealing the latter game when he picked a crosscourt backhand that he had time to return with a clean backhand winner down the line.
Murray sealed the set on serve in the next game, and the play went with serve in the fourth until Wawrinka picked the Scot's pocket to take the set on his first break point of a game Murray had led 40-15.
With Wawrinka's range increasingly deserting him -- he ended the match with 43 unforced errors against the Scot's 22 -- Murray closed out proceedings in the fourth set with two further breaks of serve.
In all, Murray converted five of 15 break points against his opponent's one from five.
(Reporting by John Stonestreet, editing by Ed Osmond)
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