Having already added defender Callum Morris to his squad on Wednesday, the Dons boss swooped for cover in arguably Aberdeen's weakest area of the park.
Lewis, 28, has signed a two-year deal after leaving Cardiff, while 38-year-old Alexander joins on a 12-month contract following his release by Hearts.
"I've got a few friends who have played in Scotland and a friend of mine Kevin McNaughton was here," said Lewis, who won a call-up to the England squad in 2008. "He told me that it's a great club and Aberdeen is a great place and that I'd really enjoy it.
"So I had no concerns about coming up here. I'm looking forward to pre-season and getting my head down and working hard."
Alexander told RedWeb: "My agent was in contact with a lot of teams and Aberdeen were one of them and I am lucky that the manager had a bit of interest in me and pursued it.
"I think as a squad Aberdeen have an all-round strength, and as a team they're good going forward, solid at the back. I've always been impressed by them and was whenever I played against Aberdeen last season."
While it is good that Aberdeen have two experienced keepers on board, many fans will be left scratching their heads about what that means for young talent Danny Rogers, and indeed who the first-choice number one is at the club.
Join the conversation about Aberdeen's goalkeeping situation on our new forum - the thread is here.