The 21-year-old is expected to travel north immediately to have his medical at United and will sign a long-term contract with the Old Trafford side worth around £90,000-a-week.
That represents a significant jump from his £10,000-a-week wages at Palace.
There was a breakthrough in United’s talks with Palace on Tuesday night and they have started organising a medical as a result.
United have also kept hold of the 25 per cent sell-on clause for Wilfried Zaha that they negotiated with Palace when he moved back to Selhurst Park.
There had been suggestions that Zaha’s sell-on clause could be part of negotiations over Wan-Bissaka.
Wan-Bissaka will be United’s second signing of the summer transfer window, with the Old Trafford side having already snapped up Daniel James from Swansea.
Ole Gunnar Solskjaer has targeted young domestic talents as he looks to rebuild his squad at United.