The statement, however, failed to clearly stipulate the "legal responsibility" which the comfort women victims have urged the Abe cabinet to express.
Yun said South Korea will consider the matter resolved "finally and irreversibly" if the steps pledged by Japan are fully carried out.
The meeting between Yun and Kishida was watched closely as the two countries have recently intensified efforts to resolve the longstanding dispute.
South Korea vowed to end the dispute once and for all if Japan fulfills its responsibilities.
The deal came less than two months after President Park Geun-hye and Abe agreed to speed up negotiations on the issue in their first summit on Nov 2.
Park had called for a resolution by the end of this year, which marks the 50th anniversary of the establishment of bilateral diplomatic relations.