The Lions will also play an historic match in Hong Kong against the famous Barbarians club on their way to Australia.
Commenting on the Lions 2013 schedule, tour manager Andy Irvine said: "The announcement of the 2013 tour schedule represents another milestone in the rich history of the British & Irish Lions.
"Since 1888 when the Lions embarked on their first ever tour, which happened to be Australia, the famous red shirt has become an aspirational symbol of achievement for players in Britain and Ireland.
"The Lions receive numerous requests to play matches around the world outside of the traditional tour destinations of Australia, New Zealand and South Africa.
"For 2013 we had the perfect opportunity to play a match in the developing rugby region of Asia, while at the same time break the long journey from Europe to Australia.
"As has become customary we also wanted 10 matches to maximise the essential pre-Test series build-up.
"The last Lions tour to Australia in 2001 heralded the dawn of 'the Red Army' with tens of thousands of English, Irish, Scottish and Welsh tourists and ex-pats wearing the red jersey in support of the Lions.
"We look forward to another challenging tour to one of the world's most beautiful countries."
Australia finished third at the recent Rugby World Cup and are currently ranked second in the world. The six-week tour will include the match against the Barbarians in Hong Kong, games against all five Australian Super Rugby teams and a clash with New South Wales Country.
Top of the bill will be the three Test matches against the Wallabies in Brisbane (June 22), Melbourne (June 29) and Sydney (July 6).
British & Irish Lions Chairman Gerald Davies said: "With the latest Rugby World Cup tournament completed, a major focus for the rugby world is now the British & Irish Lions tour to Australia in 2013.
"Lions tours are hugely popular and outside of the Rugby World Cup represent one of the game's major show pieces with global media coverage and ticket sales testament to their popularity.
"It has to be said that the last two series between the Wallabies and the British & Irish Lions have been memorable. In 1989 and 2001 both three-Test series went down to the last match.
"Of course the Lions were victorious in the series in 1989 but the Wallabies had their revenge in 2001. I am sure that the 2013 series will be just as competitive with the tour reigniting the fierce but respectful rivalry that exists between the two sides."
The last tour by the Lions to Australia was in 2001, when the Lions played ten matches including three Tests. They won seven matches, including the first Test against the Wallabies, and lost three.
These defeats were against Australia 'A' and the Wallabies in the second and third Tests. The vital third Test was won by the Wallabies 16-13 at Stadium Australia in Sydney, in front of a crowd of 84,188 to clinch the series.
Giles Morgan, Group Head of Sponsorship, HSBC Holdings plc, added: "Today marks the beginning of another exciting journey for HSBC, our staff and customers, as we build towards the British & Irish Lions tour to Australia.
"The Lions resonates particularly well with HSBC's target audience, and this sponsorship enables us to engage with four of our key markets in the UK, Ireland, Hong Kong and Australia.
"There is already great anticipation from our staff and customers around the world and with the dates and destinations now confirmed, the countdown has truly begun for what promises to be another thrilling Lions tour."
Fans can now guarantee their place on the Lions tour with Lions Rugby Travel, the official travel company of the British & Irish Lions (www.lionstour.com).
The official Lions travel company will offer fans an unprecedented range of official ticket inclusive packages from fully escorted tours through to return international flights and match ticket options.
It will also be possible for fans to create their own tour itineraries around the destinations they want to see most in Australia. For more information, fans can visit lionstour.com or call 0844 788 4070 to guarantee their place on tour now.
The venues, kick-off times and broadcasting schedule will be confirmed in due course.
2013 BRITISH & IRISH LIONS TOUR - MATCH SCHEDULE:
Saturday, June 1 -
Lions v Barbarians, Hong Kong
Wednesday, June 5 -
Lions v Western Force, Perth
Saturday, June 8 -
Lions v Queensland Reds, Brisbane
Wednesday, June 12 -
Lions v Combined New South Wales & Queensland Country, Newcastle
Saturday, June 15 -
Lions v New South Wales Waratahs, Sydney
Tuesday, June 18 -
Lions v ACT Brumbies, Canberra
Saturday, June 22 -
Lions v Australia, Brisbane
Tuesday, June 25 -
Lions v Melbourne Rebels, Melbourne
Saturday, June 29 -
Lions v Australia, Melbourne
Saturday, July 6 -
Lions v Australia, Sydney