Bath prop Stevens was removed from the England squad yesterday.
White, a former club and international team-mate of Johnson's, had originally been included in the England Saxons squad.
His place will now be taken by the promising young London Irish prop Alex Corbisiero.
Johnson added: "Julian is an experienced international. He has had time out of the England set-up but he is in good form and is ready to make the step back up to the senior squad.
"Alex was one of the outstanding players in the under-20s side that reached the final of the Junior World Championship last year.
"He has had an outstanding season for London Irish, and it's the right time to bring him into the Saxons."
White, widely regarded as one of the most destructive set-piece operators in England, will now compete with Phil Vickery for the red rose tight-head jersey he last wore against Wales in the 2007 Six Nations.