The Â£4 million development of the Church of the Epiphany, which will not have a spire or free-standing cross, will begin early next year on land donated by the Emir of Qatar, Sheikh Hamad bin Khalifa al-Thani.
The Most Rev Clive Handford, the Nicosia-based Anglican Bishop in Cyprus and the Gulf, said: "We are there as guests in a Muslim country and we wish to be sensitive to our hosts . . . but once you're inside the gates it will be quite obvious that you are in a Christian centre."
The walkways and grounds of the church, on the outskirts of the capital, Doha, will have crosses and flower motifs resembling those used in early Christian churches.
"We hope that the centre can be a base for ongoing Muslim-Christian dialogue," Bishop Handford told The Times.
Qatar's Anglican community, estimated to number between 7,000 and 10,000 people, has held services in an English-language school in Doha for decades.
The site has been levelled and a quarter of the Â£4 million needed has been raised by the Anglican community in Qatar, with the rest to be met by fundraising abroad.
The church will be run by Ian Young, a 58-year-old Scot who has served as Doha's chief Anglican priest since 1991.
Christianity disappeared from most Gulf Arab states within a few centuries of the arrival of Islam in the 7th century. But Christian expatriates have migrated to the region over the past 100 years, particularly since the discovery of oil.
Some Gulf states have allowed churches to be built, including Kuwait, Bahrain and the United Arab Emirates, where Western-friendly governments have sought to provide amenities to attract skilled expatriates.
But in Saudi Arabia, the birthplace of Islam, non-Muslim religious practice is banned.
Bishop Handford accepts that some Qataris might not be happy. "In the conservative Muslim world you'd expect it," he said. "You'd get the same in the conservative Christian world where mosques are being built."
He added: "We haven't experienced any problems or difficulties with local people. They have been welcoming and felt that this was right."
The congregation will take security precautions but no "dramatic" measures are planned. "We are pretty confident in the local security," Bishop Handford said.
Qatar, home to huge gas reserves and enjoying an economic boom, prides itself on its security. With a population of fewer than one million, centred mainly in Doha, it is confident that it can keep an eye on everybody.
An attack in March when an Egyptian engineer detonated a car packed with explosives outside a theatre popular with Westerners, killing a British man and injuring 12 other people, was viewed as an aberration. It was Qatar's only known suicide bombing.
"Already Qatar has changed from being a remote, secluded, conservative country to one that's much more open to the world," Gerald Butt, the editor of the authoritative Middle East Economic Survey, said.
Bishop Handford, a genial 68-year-old, has long experience of the Middle East, first visiting in 1956 with the RAF, when he spent time in Jordan and Iraq. Ten years later he was back as a clergyman, with posts in Baghdad, Jerusalem and Beirut.
His beat now extends from Kyrenia in northern Cyprus to Aden in Yemen. His Cyprus and Gulf diocese, unlike those of Iran, Egypt and Jerusalem, is an "entirely expatriate diocese", with no native Anglicans.