United were convinced to sign Wan-Bissaka after seeing him shackle Leroy Sane.
Solskjaer has revealed he was so impressed with the full-back's performance against Manchester City last season that he knew he could handle a move to Old Trafford.
United's manager was determined to strengthen the right side of his defence last summer, with the club's transfer committee coming up with 804 different options before narrowing down their shortlist.
They eventually paid Crystal Palace £50million for Wan-Bissaka – underlining Solskjaer's faith in the 22-year-old.
The Norwegian said: “You saw an exceptional defender when I watched him last season. He had a couple of games against Sane with Man City, and you think, 'Wow he is so hard to go past.'
“And then when you sign him you get to know him and he is a shy boy. He wants to learn."