Rooney immediately announced his playing retirement upon the appointment being confirmed.
Solskjaer said, "Great news for Wayne and I really wish him all the best.
"I think he's got everything going for him to be a good manager. He's had a very good career, he's got a very good personality and he wants to have success.
"He's played under some top managers and I'm sure he's over the moon at the moment, so congratulations to him."