The 27-year-old was top scorer in the Chinese Super League (CSL) last season, hitting 27 goals to play a major part in SIPG's maiden title success.
"The new blue and white player will wear the number 24 on his shirt," Chinese-owned Espanyol, who are in the bottom third of La Liga, said in a statement.
There was no immediate word on the size of the transfer fee.
"SIPG still follows one basic principle: as long as it (the transfer) is beneficial to the player's career and the development of Chinese football, the club will fully support it," SIPG said in a statement.
The move for the international Wu, China's best player, has been mooted for several days.
Wu, who can play centrally or out wide, was previously linked with Chinese-owned Wolverhampton Wanderers in the Premier League.
But it is Barcelona-based Espanyol who have taken the chance on a player who has spent his entire career in China at SIPG.
He outshone the likes of SIPG teammate Hulk and the Nigerian striker Odion Ighalo in the CSL last season to finish top scorer and was also named player of the year.
However, the comparisons to Argentine legend Diego Maradona -- originally made by the coach who unearthed Wu -- are way wide of the mark.
And it remains to be seen if he can make the considerable step up to Spanish football, particularly at a team who are struggling.
Espanyol lost 4-2 at home on the weekend to Real Madrid to leave them languishing in 15th place.
Wu exited with China from the Asian Cup quarter-finals last week following a 3-0 defeat to Iran.
He suffered a shoulder injury during the campaign in the United Arab Emirates, though it is not expected to keep him out of action long term.
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