Thousands of fans have stayed away this season in protest against Mike Ashley.
There was a backlash on Tyneside to the departure of manager Rafa Benitez in the summer following a lengthy stand-off with Ashley over a new deal.
Bruce called on the 11th-placed club to do something after last weekend’s 2-1 Premier League win over Southampton at St James’s Park was watched by a crowd of 42,303, United’s lowest home gate in nine years.
Speaking to Sky Sports News, head coach Bruce said: “To be fair to the club, they’ve come up with this idea, which is fantastic for truly loyal supporters of the club at this particularly hard time.
“We want a full St James’s Park. We know what it’s like when it’s full. When it’s full, it can be a pretty intimidating place.
“I think it’s a wonderful gesture from the club and also a big reward for the truly loyal support that we’ve got.
“At this particular time of year it’s tough for people to go to a football match with Christmas coming up. It’s a wonderful gesture. Well done to the ticket office as well, who I think are inundated.
“We still got the best part of 43,000 (against Southampton last weekend), quite a remarkable crowd. It’s something that we’ve tried to address. It’s something the club has thought about, and the gesture is terrific. I’m glad we can have a full St James’s Park, because that’s what it’s about. Hopefully, we can thrive off that support.”
The offer, however, was criticised by some fans. Supporter group Toon for Change called on fans to take the club up on the offer – but leave the seats unoccupied.
“We’re never going to appease everybody,” said Bruce.
“If people want to protest, its their prerogative. But I think it’s a wonderfully great gesture – 10,000 tickets is quite remarkable. I didn’t think we’d give that many away.”