The deal includes a vesting option for a second season. Financial terms weren't immediately available.
Vogt, 35, spent the past season with the Giants, hitting .263 with 10 home runs and 40 RBIs in 99 games.
"I can't begin to thank all of my teammates, coaches, front office, clubhouse staff, trainers and FANS enough for everything this past season," Vogt wrote on Twitter. "It was a season my family and I will always remember. Words will never express the gratitude we feel for the opportunity to be a Giant.
"There are many things we will miss in SF and we will treasure every memory. Thank you to all the people who had a hand in that."
Carson Kelly saw the majority of action behind the plate for Arizona last season, hitting .245 with 18 home runs and 47 RBIs in 111 games.