* Deal for Belgium's Gryson worth nearly $600 million
* Market shrinking at home, JT looks overseas for growth
* Sale includes Domingo, Fleur du Pays, Orlando brands
* JT shares up 17.5 pct since start of 2012 (Adds details)
TOKYO, May 24 (Reuters) - Japan Tobacco Inc (JT), the world's third-largest cigarette maker, said on Thursday it will buy Belgian tobacco product maker Gryson NV for 475 million euros ($597.7 million) to cut its reliance on the domestic market.
JT, which sells more than half the cigarettes smoked in Japan, has seen its home market shrink by almost 30 percent in the last decade and aims to complete the deal within the current calendar year.
Gryson has established stakes in the markets for individually made machine and hand-rolled cigarettes in several European countries, including France, Portugal and Spain.
JT will acquire all shares in Gryson, which produces filters, loose tobacco and rolling papers for brands like Domingo, Fleur du Pays and Orlando, from unlisted GT&Co BVBA using existing funds and loan facilities.
The purchase price values the transaction at 12.3 times Gryson's 2012 forecasted earnings before interest, tax, depreciation and amortization, JT said in a statement.
The company did not use a financial advisor on the deal, a JT spokeswoman said.
Shares of JT have surged 17.5 percent since the start of 2012, beating a 1.3 percent rise in the Nikkei 225 average , as Japan's government inches closer to selling part of its 50 percent JT stake.
Shares of JT rose 1.1 percent prior to the announcement on Thursday versus a 0.1 percent gain in the Nikkei benchmark.
$1 = 0.7947 euros Reporting by James Topham and Mayumi Negishi; Editing by Michael Watson and Matt Driskill