McLean left Dundee United last week, while Carey was released by St Mirren in the summer.
Manager Derek Adams, whose side visit champions Celtic for the Scottish Premiership opener on Saturday, said: “We still have maybe one more signing to make before Saturday, but Brian and Graham have come in. They have good SPL experience, they did well with St Mirren and Dundee United last season, they played a lot of games.
“Brian is an experienced centre-half. He has played in Scotland and England, he is a good organiser, comfortable on the ball and is a very good defender.
“Graham can play on the left-hand side of midfield, get forward and create chances and score goals. He is very good at set-plays and a good crosser of the ball.”