The Swede, who signed a one-year deal with United on Thursday, scored 28 goals last season, before his initial one-year deal came to an end.
United finished sixth in the Premier League, though they did win the League Cup and Europa League, and Henry told Sky Sports that Ibrahimovic will be aiming to win the title this season for Jose Mourinho's side, who have won both opening league games 4-0.
"They kept Zlatan, but I think Zlatan takes it as a challenge that he has with himself. I think he wants to do more, and he still didn't win the league.
"I know that he wants to win the Premier League, to make England another country that he conquered."
"I'm not surprised, because if I was there [at Man Utd] I would want to keep a guy like Zlatan in and around the dressing room.
"Having him around (Romelu) Lukaku, having him around Marcus Rashford [is beneficial]. Rashford was talking about it last year, he knows how to get that dressing room together.
"I'm not surprised in a way because we are talking about Zlatan Ibrahimovic, one of the best that has done it in the game, for me."
Ibrahimovic is still recovering from a serious knee injury, which cut short a superb debut season at Old Trafford in April.
The 35-year-old has posted regular, positive bulletins on his progress, and United have seen enough to sign him up until the end of the season.
He may not return until winter, but Henry believes he will work hard to gain full fitness for United for the second half of the season.
"First and foremost he already showed us that he can still perform," Henry said. "Yes, there may be a question mark with some people asking if he will return to what he was [before the injury], I have no doubt that he will.
"I know the man, and I know how he is going to work. He showed us with a couple of moves on social media, that his knee is alright. So I have no doubt with that.
"But what is important is to have a guy like that around the place. He knows what it takes to win."