The 26-year-old was widely expected to join the Swans when his Betis contract expires at the end of the month, and his move will be ratified once the transfer window opens on July 1.
The midfielder, who it is believed will join on a three-year deal, enjoyed a fine final season with Betis, helping the La Liga side secure a Europa League play-off spot. Canas will still get the chance to enjoy European competition next season as Swansea prepare to enter the Europa League following their Capital One Cup triumph.
The confirmation of Canas' signing comes in the midst of a disagreement between chairman Huw Jenkins, manager Michael Laudrup and his agent Bayram Tutumlu over the amount of money Swansea are prepared to spend on transfer targets.
Laudrup had hoped last season's success would give him the leeway to spend heavily this summer and, while Swansea are believed to be keen to back the Dane in the transfer market, they wish to retain their sensible approach to spending which has served them so well during their rise through the leagues.
There have been suggestions Laudrup could leave over the dispute, although Press Association Sport understands the club expect the Dane to be in charge next season. Jenkins and Tutumlu are set to hold further talks over the issue, and the chairman used the announcement of Canas' signing to clarify his position on the matter.
"Myself, the manager and our recruitment staff are all agreed on the quality of players we would like to sign to help us remain competitive in the Barclays Premier League," he told the club's website. "We are continuing to work behind the scenes, in private wherever and whenever we can, to strengthen our squad.
"For that reason it's disappointing that I have to respond to the speculation of unrest at the club after the fantastic season we have had. There are substantial funds available to strengthen our squad over the summer while we are also in the privileged position, because of the way we've managed our finances over the years, that we do not need to sell anyone to fund those new recruits.
"It goes without saying that some of our targets will sign for other clubs for different reasons. But that's the same for every club. The important thing, and a factor that has always been vitally important for us, is that we sign players who want to play for Swansea City for footballing reasons. If not, then we move on to the next target.
"I think most people will agree that it is a policy that has served this football club, and more importantly our fans, well over the last decade."
Source: PA
Source: PA