In a symbolic gesture before Wen's arrival, the two countries signed an agreement allowing the resumption of Japanese rice exports to China.
The exports had been halted since 2003 when China revised quarantine rules.
During his visit Wen plans to address the Japanese parliament and issue a joint statement with Abe expressing their hopes for building "a strategic and mutually beneficial relationship".
"I feel strongly that my trip has a real mission"
According to Japanese media reports, the statement will look to set aside the countries' clashes over territory and wartime history and focus on areas where they can work together.
Also on the agenda during the visit are talks on strengthening economic ties, collaboration on energy conservation and military co-operation.
Efforts to rein in North Korea's nuclear programme are also likely to be discussed.
The visit is being seen as evidence that ties between the neighbours are on the mend after a series of rows related to Japan's wartime past.
In 2005 the long-festering dispute erupted into violent anti-Japanese protests in China, including a brief siege of the Japanese consulate in Shanghai.
Wen's trip to Japan follows a fence-mending visit by Abe to Beijing last year, after which both sides have stepped up efforts to put relations back on track.
Visit's by Abe's predecessor, Junichiro Koizumi, to Tokyo's Yasakuni shrine had been a focus of fierce criticism from China.
The shrine honours Japan's war dead, including several convicted war criminals.
Since coming to office, Abe has avoided going to the shrine, although he has not ruled out visiting in future.