James Rodriguez, who shone for Colombia in the recent Copa America, has returned to the Spanish league, signing for Madrid club Rayo Vallecano, who are celebrating their centennial season.

The 33-year-old playmaker, who won the Golden Boot at the 2014 World Cup, played in La Liga from 2014-2020 with Real Madrid.

Rodriguez had his contract with Brazilian club Sao Paulo rescinded after he led Colombia to a runner-up finish in the Copa America.

"I feel great joy to join a historic club like Rayo," Rodriguez, said. "I really want to do things well. I feel that responsibility wherever I go. I like to win. Especially in such an important year for the club."

Premier League Brighton have signed Denmark midfielder Matt O'Riley from Celtic. The London-born 23-year-old began at Fulham and played for England at youth and Under-21 level before opting to play for Denmark, the native country of his mother.

After helping Celtic win the Scottish league title in each of the past three seasons he moved for a reported Stg 25m ($A49 m) fee and signed a five year deal.

"He enjoys getting forward and attacking the opponent's penalty area, but he also has a good defensive instinct," Brighton coach Fabian Hurzeler said. "That balance makes him special."