Klukowski, who has been in interim charge since the beginning of February following the departure of Josh Gowling, has impressed since taking the reins temporarily.
Since taking over he has overseen a purple patch for the Bulls - winning three from his first five games including a win at leaders AFC Fylde last week.
Jared Hodgkiss will also stay on as player-coach.
"I have enjoyed taking charge of the team so far and would like to thank the players for their support and effort," Klukowski told the club's website.
"Their attitudes have been fantastic and our recent wins have been down to their hard work.
"I’d also like to thank Jared and the rest of the staff who have been a great help and support to me, and of course to the fans who have offered some very kind messages of support.
"We will continue to work hard and do our best for the club."
Hereford General Manager, Jamie Griffiths added: "We’d like to thank Yan for his efforts and commitment during his interim period and thank him for accepting our offer to remain as manager for the remainder of the season.
"This provides stability in what has been an unsettling time. Results and performances have been encouraging, and it is clear that he has the respect of the players and staff."
The new permanent boss has a tough test ahead of him straight away - Hereford host Chester tonight looking to make ground on the top seven.