Bryce has signed for the Major League Rugby side LA Giltinis and will move to Los Angeles later this month when his current deal expires.
He follows former Warriors team-mates Adam Ashe and DTH van Der Merwe in moving to the American club.
Wilson said: “Glenn's been outstanding for us in this period. He’s been one of our best backs, so I desperately wanted him to stay for the rest of the season.
“We did make an offer to try and keep him here but he had a really good opportunity elsewhere, which he took.
“Also for Glenn, it’s a great life opportunity. But Glenn has conducted himself well in my short time with him, and has played well for us.”
Bryce, 29, is in his second stint at Glasgow Warriors and also had a spell at Edinburgh. He returned to Scotstoun on a short-term deal at the start of this season and performed well at full-back. He has been named on the bench for Friday’s 1872 Cup second leg home match against the capital side.
He was a regular at full-back earlier this season but the redeployment of Huw Jones at full-back has limited his starting opportunities. Jones, initially a centre, is out of contract at the end of the season.
“I don't have any update on him or anyone else at the moment,” said Wilson. “We will start to make some updates and announcements but right now I have nothing I can confirm or deny.”
Meanwhile, Glasgow’s Scotland centre Sam Johnson will miss the match as he is isolating. His place will be taken by Scotland sevens specialist Robbie Fergusson.
“Sam Johnson is a Covid situation,” explained Wilson. “He trained yesterday and then became a close contact last night, which led to Sam being unavailable.
“It's a massive blow but then Robbie Fergusson gets a chance in a derby having played really well for us for four games earlier in the season.”