Melrose will acquire the ventilation product maker for $86 per share.
The merger agreement was unanimously approved by Nortek's and Melrose's boards of directors.
"We are very pleased to have reached the proposed agreement with Melrose Industries, which represents a significant premium for our shareholders," Nortek's CEO Michael Clarke said. "We believe this transaction will be a positive for our employees and customers alike."
The deal will divide Nortek's debt in half and free up cash for the company. The acquisition gives Melrose access to Nortek's ventilation and home security business.
"We are convinced we can steer this fine business to achieve its full potential," Melrose's Chairman Christopher Miller said.
Nortek's shares have climbed more than 98 percent year to date.
Nortek's year-to-date performance:
—Reuters contributed to this article.