The Swede was appointed Pirates coach on Monday as the club endures its worst run in the PSL - punctuated by a record 6-0 loss to Mamelodi Sundowns this month - and risks finishing outside of the top eight this season.
The 39-year-old Nomvethe worked with Jonevret when he was in charge of Djurgadens IF, winning the Allsvenskan (Swedish league title) and Svenska Cupen (league cup) in 2005, before 'Bhele' returned to South Africa to join Bucs.
Nomvethe, who is showing no signs of slowing down with 11 goals to his name in the NFD for AmaZulu this season, believes Pirates will gain much under Jonevret's tenure.
"He's a good coach and he's a coach who's not aggressive, but he wants the job to be done," Nomvethe tells KickOff.com.
"He also wants to see his players work hard and demands dedication because he wants to see positive results at the end of the day.
"When I joined him [at Djurgadens] we won the league title in Sweden and the cup when he was the coach at the club. But then I left to come to South Africa to join Orlando Pirates, and I left when the team was still in good shape and doing well."
Jonevret was named Swedish Manager of the Year in 2005 but has never coached in Africa before, and with Pirates at a low point he faces testing times at Mayfair.
"The situation right now is not good for him at Pirates," adds Nomvethe.
"But I'm sure he'll do all he can in his power. But we cannot say now he can change things quickly all of a sudden. But I can assure he'll leave a good mark there."
Jonevret's first assignment is against Polokwane City at Orlando Stadium on Saturday, having just received his work permit.