"It's a great opportunity to join this club and to play for the first time in the Spanish league," Andersen was quoted as saying on the Betis website.
"They have had a very good season and have qualified for the Europa League. I know they have fantastic supporters and a great tradition."
The 30-year-old, who joins from French Ligue 1 side Evian Thonon Gaillard, represented Denmark at the 2010 World Cup and at Euro 2004 and 2010.
The former Charlton Athletic and Brondby player will be presented in July, the club said. Betis finished seventh in La Liga last season.
- Sports & Recreation
- Europa League
- Evian Thonon Gaillard