Austrian Hasenhuttl, who coached RB Leipzig and Ingolstadt in the Bundesliga before a four-year spell at Southampton in the Premier League until 2022, will officially be presented on Monday.
Earlier on Sunday, Wolfsburg managing director Marcel Schaefer said a change of coach was needed "to give the team a new impulse, in order to stabilise the situation".
Wolfsburg's last league win dates back to December 16th and the team have now gone 11 consecutive Bundesliga matches without a victory. Saturday's defeat sent the Wolves down to 14th in the league.
"(Hasenhuttl) signed a longer contract with the club and will lead training from Tuesday onwards," Wolfsburg said. It gave no details on the duration of the deal.
Kovac, a former Croatia international who also coached Bayern Munich in 2018-19, took over at Wolfsburg ahead of the 2022/23 campaign and led them to an eighth-place finish in his first season in charge.
This season, however, has been anything but successful with the team currently on 25 points, six above the relegation playoff spot.
