The 31-year-old left the Yellow Submarine following their relegation in the summer and has been without a club ever since.
He passed his medical with the Seville club earlier on Thursday and subsequently posted a picture on Twitter of himself signing his contract.
The picture was accompanied by the words: "Excited to get to a big club! I'm looking forward to it. Mucho Betis!"
Angel, who won five senior caps for Spain in 2006 and 2007, missed much of last season with a torn cruciate ligament but his new club confirmed: "Angel arrives in optimum fitness, offering very satisfactory data in the medical examination."
He has played over 200 games in the Primera Division during his career and can operate in either full-back position or as a holding midfielder.