Williams has attracted plenty of interest since his first-team breakthrough in 2014-15, with Manchester City and Liverpool linked with a move, but has agreed to extend his stay at the San Mames.
The 21-year-old's buy-out fee has been set at €50 million.
Williams earned promotion from the B team after scoring 13 goals in 18 Segunda B appearances at the beginning of last season and started the Copa del Rey final defeat to Barcelona.
The Bilbao-born youngster has impressed in his maiden full campaign under Ernesto Valverde, scoring six goals in 15 appearances so far.
