The four-time Grammy award winner will perform in Hobart on March 28 alongside The Cranberries and Wolfmother.

Tickets for the concert will go on sale on Monday.

Kravitz will be in the country playing two concerts in Sydney to coincide with the Australian F1 grand prix on March 17 and 18.

He will also perform in Wollongong on March 20, Sydney on March 21 and in Brisbane on March 24.

“We received an overwhelming demand to take the show to Tasmania and couldn’t deny the fans," promotor Andrew McManus, of McManus Entertainment, said.

"It has been 18 years since Lenny Kravitz last toured Australia - Lenny is an international superstar and it’s a pleasure to bring him to Tasmania."

Kravitz has sold more than 35 million albums worldwide, has recorded eight studio albums with hit songs such as Are You Gonna Go My Way, American Woman and Let Love Rule.

The Cranberries, from Ireland, shot to prominence in Australia in 1994 with their number-one album No Need To Argue and To The Faithful Departed (1996) and hit singles Linger, Dreams and Zombie.

Australian rockers Wolfmother won a Grammy in 2007 for Best Hard Rock Performance for their single Woman and followed it up with ARIA Award wins for Best Group, Best Breakthrough Album and Best Rock Album for their debut self-titled album.

Tickets for the Hobart concert go on sale MOnday, February 13 at Ticketmaster www.ticketmaster.com.au or 136 100.