United landed the England U-21 star from Crystal Palace last week in a £50m deal.
The fallen giants have also signed Wales international Daniel James from Swansea for £15m.
Solskjaer is still keen to make more signings before the start of the new season as he bids to make United serious contenders once again.
United have opened talks with Sporting Lisbon about a £50m deal for midfielder Bruno Fernandes and have also targeted a new centre back.
But Solskjaer admits he is delighted with the business United have done so far – and is expecting big things from both Wan-Bissaka and James.
He said: “Both these players have the X-factor, real X-factors.
“They are great human beings who are hungry, hard working and just at the start of their careers.
“Of course we don’t expect them to set the world alight on the first day.
“Over the summer I have been in touch with Ed Woodward (executive vice chairman) and Joel Glazer (co-owner) and all the recruitment people”
Ole Gunnar Solskjaer
“But they are going to grow into big and very good players for Manchester United.”
Solskjaer, who jets to Australia this weekend to begin the club’s summer tour, still wants more signings before the big kick off.
He added: “We are always looking to improve the squad.
“Over the summer I have been in touch with Ed Woodward (executive vice chairman) and Joel Glazer (co-owner) and all the recruitment people.
“I’ve got to say it’s been very good so far.
“I’ve got the backing and we’ve got the people in we wanted to, for now, and there will probably be some more business being done.”
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