The 23-year-old forward, who watched from the stands as the Robins beat Crystal Palace 4-1 last night, has signed a three-year deal at Ashton Gate.
"I'm so pleased to have signed Sam Baldock because I believe he will add sharpness to our attack and keep opposing centre-backs occupied," said McInnes.
"He can link the play, but his best work is done on the move and he is capable of teaming up effectively with different types of strike partners.
"With Steve Davies having signed for us as well this week, we now have a lot more attacking options."
West Ham are believed to have received a fee in the region of £1m from Baldock's sale.