Terms were agreed with the 26-year-old on Tuesday night after the Warriors had an offer accepted by Forfar last week.
Munro will be available for Saturday's Scottish Cup fourth round tie at Aberdeen and Stenny boss Colin McMenamin said he was delighted to land a player he had been targeting for some time.
He said: "We identified Andy as a key target a few weeks ago and have worked hard to get a deal through as quickly as we could.
"Andy is a strong and aggressive defender with plenty experience at this level and he is a player who can make a difference both now and going into next season.
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"I think the fans will like what they see, he is a winner, a leader and was our number one target for this position going into the window."
Munro began his career with Raith Rovers before moving to Arbroath and then Forfar. He also had a successful spell on loan at Clyde this season.
He worked with McMenamin's assistant manager Stuart Balmer at Forfar and said that was a big factor in his decision to sign.
McMenamin is also hoping to bring in a striker fowlloing his decision to quit playing and concentrate on management.