Pack the cat tray, litter, feeding dishes, favourite toys, food and a blanket or something else that smells familiar in a box that goes into the car or removal van LAST and comes in FIRST.
Put cat into a room with the contents of that box and close the door firmly. Affix a notice to door saying "Do NOT open, the cat must be kept in"
If the cats do not already know each other well all this has to be done twice in separate rooms.
I kept mine in for a fortnight after the move, then got out their harnesses and leads. The bolder was thrilled to go round half of the garden with me on his lead, his brother ran away and hid when he saw the lead, so we left him indoors. A couple of days later he was ready to go out too.
For the next couple of weeks, the cats were out without their leads, but only when I was in the garden near them.
Let them explore the house thoroughly before going out,
If your and your partner's cats are not friends, you may need to keep them separate for at least a fortnight. When you let them be in the same room, you can avoid jealousy if you cuddle your cat and he his for quite a while.