The pair moved to Upton Park from Liverpool, with 29-year-old winger Downing joining on Tuesday after agreeing a four-year deal.
Allardyce believes the duo, who join the club's three other recent signings Razvan Rat, Adrian and Danny Whitehead at Upton Park, can help improve his side.
"To pick up two players of the quality of Stewart and Andy is good business both financially and in football terms, and they will help to improve us as an attacking unit," Allardyce told the club's official website.
"Stewart is a great player with a very good pedigree," he continued.
"If you look at his technical and physical stats, it puts him right up there among the top players we have at the club.
"He's a talented boy with good energy, and will improve the team quality, particularly in possession. He doesn't give the ball away, he can hold it if he needs to and he can dribble as well.
"Stewart will be able to produce the kind of ball we need, and will have the opportunity to cross the ball, just as he did at Aston Villa."
West Ham get their Premier League campaign under way on Saturday against Cardiff City.
