However, the Trust has at the same time called on owner Vincent Tan to honour his promise to meet with fans' groups.
Solskjaer, 40, was presented to the media on Thursday as he succeeded Malky Mackay as Bluebirds' boss just six days after the Scot was sacked.
Mackay's dismissal had caused uproar among Cardiff fans but many are pleased by the decision to bring in former Manchester United striker and Molde coach Solskjaer.
The move has won praise from the Trust, who now hope to meet Tan after a previous meeting, scheduled for Saturday's game against Sunderland - just a day after Mackay lost his job - was cancelled.
The trust statement read: "Ole Gunnar Solskjaer is an exciting appointment as the new Cardiff City manager. It is important that he is now left to get on with the difficult task of ensuring the Bluebirds' status as a Premier League club is secured. We wish him well.
"Given what has happened at the club over the last couple of months, there is need for a period of stability. It is important that fans get behind the new manager and players as they strive to move up the Premier League table.
"Following Ole Gunnar's appointment, we trust Mr Tan will now fulfil his pledge to meet the Trust and the Supporters' Club to discuss a range of issues which fans are concerned about. We hope Mr Tan will also look to build bridges with supporters.
"It is absolutely crucial that regular dialogue takes place between Mr Tan, supporter organisations and the fans generally."