The meeting was held last week at the Ecumenical Center in Geneva, Switzerland, where the WCC's headquarters are located.
It was the first meeting between the two bodies since the Global Christian Forum in Limuru, Kenya, in 2007.
The meeting was also the first since Dr Tveit took over as general secretary of the WCC in January.
The two leaders discussed areas of common interest and collaboration, including mission and evangelism and the ongoing work on a code of conduct on conversion, which also involves the Roman Catholic Church.
"We affirmed that all Christians have a common call to be one, and that we want to be sensitive to one another's concerns," Dr Tveit said of the meeting.
Dr Tunnicliffe said: "This important meeting was helpful in building bridges of understanding in regards to evangelism, religious liberty and caring for the vulnerable. We look forward to ongoing conversations with the WCC."
The two leaders affirmed the continued support of the WCC and WEA for the relatively new Global Christian Forum as a platform providing opportunities for encounters and dialogue between Orthodox, Catholic, Anglican, Protestant, Evangelical, Pentecostal and the African Instituted Churches.