The 30-year-old Johnson, who converted 50 of 59 opportunities and tied Atlanta's Craig Kimbrel for the major league lead in saves this past season, was emotional about leaving Baltimore.
"It actually just hit me five minutes ago," Johnson told MLB.com and MASNSports.com on Tuesday morning, pausing periodically to collect himself. "Really, I'm not like this. Obviously, watching the changes [in the organization] in the last couple of years being a big part of it. ...
"It's been great playing there and for all my teammates, and watching that city transform the last couple years, I take great pride in that. Obviously, I have great memories looking back."
Johnson, who joined the Orioles in 2006, was 3-8 with a 2.94 ERA last season. He also led the majors with 51 saves and was an All-Star in 2012.
Meanwhile, the AL West champion Athletics have found their closer to replace All-Star Grant Balfour, who became a free agent after the season.
Although general manager Billy Beane had confidence he could have filled the ninth-inning duties from within, he was able to find Balfour's replacement via trade -- a common December practice for the GM and low-budget club.
The A's fortified their rotation Monday, as well, reaching a two-year, $22 million agreement with free-agent left-hander Scott Kazmir, sources told ESPN's Jim Bowden and Buster Olney.
Information from The Associated Press was used in this report.