Sturridge, who struggled to hold down a regular first-team place after joining Chelsea from Manchester City in 2009, scored after seven minutes on his debut in the FA Cup victory over minor league Mansfield Town on Sunday.
Henderson predicted a bright future at Liverpool for his fellow England international.
"He's definitely made the right choice in coming here and I think he'll be a top player for Liverpool," Henderson told the club's website (www.liverpoolfc.com) on Friday.
"I thought he was really good (against Mansfield). He hadn't played for a while but he was really sharp, he got his goal. He is a big talent.
"I think it's a great signing and he'll do really well."
Sturridge, who started 49 games and made 47 substitute appearances in three-and-a-half years at Stamford Bridge, scoring 24 goals, is set to form a lethal partnership up front with Uruguayan Luis Suarez.
Henderson said he had played a small part in persuading the striker, whom he knows from the England set-up, to join.
"It wasn't anything much," said Henderson. "Just telling him what it's like, but Liverpool speaks for itself as a club and city. It's got great people here, the city's great and the club is massive."
Sturridge has won four England caps and featured in the British team at the 2012 London Olympics after overcoming a bout of meningitis. (Writing by Justin Palmer, editing by Clare Fallon)
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