The former Manchester United frontman, 29, will fly to London to finalise personal terms and have a medical.
It is understood Stoke have accepted a fee in the region of £24m. In May, Hernandez – widely known by the nickname Chicharito, which means ‘little pea’ – became Mexico’s leading all-time scorer with his 47th international goal.
Hernandez scored 59 goals in 156 appearances for United after arriving at Old Trafford in 2010, before joining Leverkusen for £7.3m in August 2015.
He has netted 39 times in 76 matches for the German club.
West Ham signed Manchester City and England goalkeeper Joe Harton a season-long loan deal on Tuesday.
Bilic has been desperate to sign a forward after injuries to Andy Carroll and Diafra Sakho meant West Ham ended last season with on-loan Jonathan Calleri, who scored one deflected goal in 19 appearances, playing in attack.
Assuming the move goes through as planned, Hernendez could make his West Ham debut against former club United at Old Trafford on August 13.
Meanwhile, Austria forward Marko Arnautovic is due to have a medical in the next 48 hours after the Hammers agreed a deal with Stoke City.
Arnautovic, 28, joined Stoke from Werder Bremen four years ago and is just 12 months into a four-year contract with the Potters.
He scored seven times in 35 games in all competitions last season.