The Englishman was not a favourite of former United manager Jose Mourinho.
And Solskjaer says the improvement is down to Shaw feeling better mentally and physically.
"Luke has immense quality," said Solskjaer. "You saw the few times against Liverpool when he takes the ball and drives forward.
"It's something that I've pushed him to do more, because we know he can do it.
"He's mentally very good at the moment. He's become a dad, he's physically very good and his fitness is so much better.
"When you have the talent of Luke, when that fitness and mental bit is sorted, you're always going to get good performances.
"Luke's a boy I enjoy talking to, I enjoy trying to help him, he wants to be better. It was about getting him to enjoy his football.
"We know his talent, but it was trusting his fitness injury-wise, having players who can back him up.
"Both Brandon Williams and Alex Telles coming in have given him a little bit of a push to say 'if you're not performing then I have good options'."