The defender penned new terms this week.
Solskjaer is delighted, insisting there's a confidence Bailly will overcome his long-term injury problems.
He said today: "Eric has been showing that he is more and more resilient, more robust.
"He has shown throughout the season he is maturing and we want to get the best out of him. He is highly regarded, the boys love him. He never lets us down.
"He is improving with the ball, very pleased he is staying."