The 53-year-old guitarist was previously married to "One Day at a Time" actress Valerie Bertinelli, with whom he has a 17-year-old son named Wolfgang. He and Bertinelli separated in 2001 after 20 years of marriage. Their divorce was finalized last year.
This will be Liszewski's first trip down the aisle.
People.com said Van Halen dropped to one knee and proposed to Liszewski while they were vacationing in Hawaii in early August. The couple plans to marry next June, a source told the magazine.
"They are happy, healthy, very much in love and looking forward to living life together forever," the insider said. "They are devoted to each other and to experiencing life in a whole new, positive and passionate way."
Van Halen underwent tests for an undisclosed illness this year and was treated for tongue cancer in 2002.