What size rims do i need for a (700x23c) 23-622 continental ultra race road bike tires?

hi i both this old road bike to make a fixie, but it didn't have any tires.
i went and also both some (700x23c) 23-622 continental ultra race road bike tires, but it does not seems to fit the bikes rims or wheels,
what size wheels (rims) do i need to buy to make the tires fit.
(i.e. i can't change the tires because i both it from a guy and he wouldn't take them back)

thanks for your time