Saints had already agreed a pre-contract with the 22-year-old centre-back and have now signed him after agreeing an undisclosed fee with Inverness.
A statement on the club's official website read: "The former Celtic academy graduate has signed a two-and-a-half-year-deal until the summer of 2022.
"Jamie is the son of former Motherwell defender Chris McCart and goes straight into the squad for tomorrow night's clash with Celtic at McDiarmid Park subject to SFA clearance."
The signing comes days after manager Tommy Wright criticised the club's hierarchy over the lack of transfer window activity.
McCart faces a fight to get into the Saints team. The Perth side have only conceded three goals in eight games and lost once in that period, with Saturday's 2-1 win over Kilmarnock taking them five points away from the bottom two.
Speaking ahead of the visit of the Ladbrokes Premiership leaders, goalkeeper Zander Clark said: "The boys are all confident. We are coming off the back of a good result at the weekend, one where we had to dig in deep to get.
"We controlled the game for large spells and it gives us a boost going into
"We need to make sure we have the same sort of performance level that we had at the weekend. We need to be brave on the ball, try and retain possession and try and make the pass in the build-up play count.
"We need to make sure we are solid in defence again and takes chances when we create them."