Chmerkovskiy, 34, shared a photo of himself and Johnson eating wedding cake in bed.
"I am so grateful that it's you that I get to call my wife, that it's you I get to wake up next to, that it's you I get to love for life, you I get to have and eat my cake too," the star captioned the post.
"Rhyme aside, I love you dearly, lucky to have you and hold you near me. What a privilege I've been given, you're gods gift that keeps on giving," he added.
Chmerkovskiy said he "can't imagine" loving Johnson more and promised to love Johnson "from now until eternity."
"Happy April 13th, our wedding anniversary," he concluded.
FOLLOW REALITY TV WORLD ON THE ALL-NEW GOOGLE NEWS!
Reality TV World is now available on the all-new Google News app and website. Click here to visit our Google News page, and then click FOLLOW to add us as a news source!
Johnson said in a post on her own account that the past year with Chmerkovskiy has been the "greatest year" of her life.
The couple have been self-isolating amid the coronavirus pandemic.
"Happy 1st Anniversary my love.. crazy to think that exactly a year ago we were celebrating with all of our closest friends and family! And although this isn't how we were meant to spend our first anniversary, I'm incredibly grateful to spend it snuggled up to you safe and sound," Johnson said.
Copyright 2020 United Press International, Inc. (UPI). Any reproduction, republication, redistribution and/or modification of any UPI content is expressly prohibited without UPI's prior written consent.