The Spaniard seems to have agreed a Bosman deal with the Premier League outfit with his contract at Estadio Benito Villamarin due to expire at the end of the current campaign.
Swansea attempted to sign the holding midfielder in the January transfer window, but the transfer failed to materialize.
The 25-year-old is set to become the fifth player from Spain at Liberty Stadium, with Michu, Pablo Hernandez, Chico Flores and Angel Rangel already on the books.
Jose Canas has spent his entire career at Real Betis, making a total of 64 league appearances for los Verdiblancos.
He managed to nail down a regular starting berth shortly after the club gained promotion to La Liga two years back and has started 24 league fixtures this term.