Hamish McColl and Sean Foley played the comedy duo
Celebrities including Ben Elton, Barry Humphries, Angus Deayton and Richard Briers were in the audience to see the show's opening night at London's Wyndham Theatre.
And the critics have given the show a unanimous thumbs-up.
"Incredibly funny," wrote Jonathan Myerson in the Independent - while the Times' Caitlin Moran called it "96% genius".
Triumph
The Daily Mail's Michael Coveney said it was "the funniest and most inventive new comedy of the year".
Branagh's directorial triumph comes a day after winning an Emmy best actor award for his role in the film Conspiracy.
The Play What I Wrote has also earned plaudits for comedians Sean Foley and Hamish McColl - who star in the show.
The play, written by Foley and McColl - and based on material by Morecambe and Wise scriptwriter Eddie Braben - centres on the duo's attempts to get a real-life celebrity to appear in one of Ernie Wise's own appalling plays.
Stars
Branagh has lined up a series of surprise celebrities to make an appearance during the play's run at the Wyndham Thetare - including, it is reported, Victoria Beckham and Kylie Minogue.
Other said to be in discussions with the play's producers include actors Richard E Grant, Keanu Reeves and Jude Law, model Naomi Campbell and comedian Frank Skinner.
On Monday night film star Ralph Fiennes guested.
Fiennes told BBC Breakfast: "It seemed like a fun thing to do, and the script is very funny and the guys are amazing."
Actor Richard Briers, who was in the audience for the opening night, said: "It's so funny we all laughed for one hour and 55 minutes without stopping - it's just a lovely, lovely show."
Morecambe and Wise were one of the best-loved comedy acts the UK ever produced, and appeared regularly on BBC TV for many years.
Eric Morecambe died in 1984, and Ernie Wise in 1999.