The winger has penned a four-and-a-half year contract and becomes one of the highest paid players in Wolves' history in the process.
The previous record was set just last summer when Ivan Cavaleiro joined for £7m.
Costa has starred for Wolves since joining from Benfica on loan for the season, netting nine goals and providing a host of assists including two in Saturday's famous 2-1 win at Liverpool in the FA Cup.
The deal takes Fosun's spending since buying the club, on transfer fees alone, to £27m.
Wolves have moved to secure the Portuguese player on a permanent basis with the Premier League vultures circling.
Everton and West Ham are thought to have shown an interest but no other club could buy Costa during the current January transfer window, as part of the season-long loan agreement with Benfica.
That wasn't going to be the case in the summer, though. But Wolves will now either be able to keep Costa as they plot a course for promotion, or sell him for a sizeable profit.
Costa said he was 'very happy' to have put pen to paper on a four-and-a-half year contract.
"I am very happy to have signed this deal," he said.
"I am enjoying every moment here at Wolves and now I want to get back to work and help get Wolves back up to the Premier League.
"The fans have been incredible both to me and to the team.
"We are going to do our best and keep pushing to the end of the season."
Boss Paul Lambert spoke last week about how he would love to sign Costa on a permanent deal.
He said today: "Going forward this is a big statement by the owners.
"This is great news for Helder, great news for the club, and great news for the supporters," said Lambert.
"For how good he has been for Wolves, Wolves have been great for Helder as well.
"Helder is well respected by everyone at the club and is playing at the top of his game at the minute.
"For the owners and everyone connected with the club it is a big situation for us to get him signed.
"It is vital for him to keep playing as he is.
"He has got ability, no doubt about it, and if he keeps up the workrate to go with that ability then he has a big chance to be a really top player."
Sporting director Kevin Thelwell added: "He is a top, top player and to have him at Wolves is an absolute delight.
"I know I said not long ago that it looked as if it would be difficult to sign Helder, but things change in football, and it is great that the deal has now been done.
"Fosun had invested heavily in the football club last summer, and so to push the button on investing heavily again in this window is something that we maybe didn't think would be possible.
"It is fantastic that they are showing such a high level of support by doing this, and such a high level of ambition.
"Recruiting players of this quality is really important for our future and it is fantastic to be in the position of making a record signing in the January window who we know is going to do the business for us."