The 20-year-old travelled to Italy on Monday to undergo a medical with the Serie A outfit, and has now penned a five-year contract with his new club.
Sampdoria are believed to have paid Leeds an initial £5.8m up front, with another £400,000 due in various add-ons, although this has not been confirmed by either club.
Vieira came through the youth system at Elland Road, and leaves Leeds having made 71 first-team appearances.
The midfielder only penned a four-year extension with the Whites last summer, but has been allowed to depart ahead of the 2018-19 Championship season, which gets underway this weekend.
"We wish Ronaldo and his family every success for the future," read a statement on Leeds's official website.
Vieira has been capped on three occasions by England's Under-21 outfit.