The French striker has endured something of a rollercoaster ride at Old Trafford since arriving from Monaco in 2015, with three managers and different roles on the pitch.
But the 24-year-old is enjoying his best goalscoring season for the Red Devils with 19 goals in all competitions - with 14 coming in 25 appearances in the Premier League.
Martial looked in fine form as he bagged all three goals in United's 3-0 win over the Blades and ahead of their trip to Brighton on Tuesday, Solskjaer says he is happy to see Martial in a positive mindset.
"He's playing with a smile on his face," Solskjaer told Sky Sports.
"Anthony has had a really good season, he's been really important for us. We felt it during the couple of months he was out injured; we struggled.
"But he knows that we trust him. He knows that we'll have patience with him and that we'll keep working with him."
While Martial has always operated through the middle under the Norwegian, Solskjaer believes his positional work in training is behind his improved form.
"He's a good finisher but it's about being in and around the right positions," he added.
"He's developed more and more in terms of getting into that penalty area and closer to the goal.
"We do a lot of work in finishing groups and sessions but it's also down to him to be mentally sharp and ready. We've always known he's a quality player and highly, highly skilful."