The Dodgers didn't disclose financial details of the agreement. League sources told ESPN and the Los Angeles Times that Nelson has a $1.25 million contract that includes a $2 million club option for 2021.
The 2021 option could become a more lucrative mutual option if Nelson reaches certain performance-based goals. According to ESPN, his deal could exceed $13 million if he hits all of his incentives.
Nelson, a second-round pick of the Brewers in the 2010 MLB Draft, spent the past six seasons in Milwaukee. He broke out as a starting pitcher in 2017, posting a 12-6 record and 3.49 ERA while finishing ninth in National League Cy Young Award voting.
Nelson, 30, underwent major shoulder surgery in September 2017 and missed the entire 2018 season. This past season, he pitched in only 10 games because of an elbow issue.
The Brewers opted not to tender Nelson a contract in December, making him a free agent.
Nelson has a 33-46 record with a 4.22 ERA and 578 strikeouts in 107 career starts with the Brewers.