The Ecuador international moves to Sunderland for €20m.
Angulo, 22, has penned a four-and-a-half-year contract on Wearside, with the option of a further year.
"Nilson is an incredibly exciting prospect, and we are delighted he's chosen to join Sunderland," said Sunderland sporting director Kristjaan Speakman.
"A quick and creative wide player, he excels in all the core actions required to impact the final third, and he arrives ambitious to make an impression.
"He's young but has already had many interesting experiences as a senior player domestically, on the European stage, and internationally with Ecuador.
"We are delighted to have completed this signing and look forward to welcoming Nilson to Wearside."
