Morrisons is at the centre of a bid battle between two US private equity firms.
The supermarket group agreed a £7bn offer from Clayton, Dubilier & Rice (C,D&R) in August, but a rival consortium led by Fortress could still trump the bid and the battle looks to be heading for an auction.
Chairman of the trustees, Steve Southern, said that under CD&R, the outcome for Morrisons pensioners would be positive.
"We are pleased with the progress made and CD&R's ability to provide the necessary support and reassurance to the schemes," he said.
"CD&R has been proactive in its engagement with the trustees, with discussions progressing positively and decisively, delivering a positive outcome for all members of Morrisons' pension schemes."
Sir Terry Leahy, senior adviser to CD&R funds, added: "We are delighted to have reached agreement with the trustees, providing additional security and covenant support to the schemes.
"We thank the trustees for their constructive engagement, and the positive outcome underscores CD&R's approach as a responsible investor and emphasises the respectful approach CD&R would take to its wider stakeholder responsibilities and commitments."