The 49-year-old is set for a second spell in charge of los Leones and will return to the club this week
The 49-year-old boss spent two years as los Leones coach from 2003 until 2005 and spent six years of his playing career at San Mames.
The trainer parted ways with Valencia at the start of June following a six-month spells in charge at the Mestalla, after failing to secure Champions League football next season with a fifth-placed Liga finish and will succeed Marcelo Bielsa at Atleti.
"Athletic Bilbao and Ernesto Valverde have reached an agreement for him to be our new coach of the first team," the club's website stated.
Club president Josu Urrutia will present the trainer to the media on Friday ahead of his second spell as coach at the club.
Bielsa left the Bilbao-based club earlier in June after failing to earn a contract extension on the back of a 12th-placed Liga finish, one season after the club reached the Copa del Rey and Europa League finals.
Valverde left Bilbao eight years ago and has since enjoyed spells at Espanyol, Olympiakos and Villarreal.