Chiefs head coach Dave Rennie said the international match would fall in a crucial time for his side's Investec Super Rugby campaign.
"The chance for provincial players to play against international sides is a rarity in the professional era, so we are really excited by the challenge.
"Gats is hugely respected in this community so it's a nice fit for him to bring his Welsh team home to Hamilton to take on the Chiefs."
Gatland said it was great the Tuesday evening match had been confirmed.
"For the squad it will be a great opportunity to have further game time together ahead of the second and third tests against the All Blacks.
"For me personally it will be an honour to bring Wales to Hamilton and face the Chiefs."
The kick-off time will be confirmed shortly.
Gallagher Chiefs and Waikato rugby memberships are available with the option to include the Chiefs v Wales match. Current members are invited to renew now and new membership inquiries can be made through www.chiefs.co.nz.