The review, commissioned a year ago, was chaired by the former Bishop of Oxford, Lord Harries.
He was assisted by Professor Charles Handy, a former professor at the London Business School; and Professor Patricia Peattie, a former chairwoman of the Episcopal Church of Scotland's standing committee.
The review team consulted widely: it held meetings in all six Welsh dioceses, which, together, were attended by more than 1000 people. It received written submissions; and it held meetings with senior clergy, bishops' advisers, ordinands, and staff from St Michael's College, Cardiff. It also met a delegation of young people.
The report's recommendations include: replacing parishes with much larger "ministry areas" served by a team of clergy and laypeople; using church buildings for multiple purposes; training laypeople to take more leadship roles; and increasing the range of worship, in order to "resonate with those unfamiliar with church culture".
Dr Morgan said that many "internal reports" had already been conducted about the state of the Church in Wales, but, "because they come from inside, the Church has taken them seriously but refused to act on them".
The three people who conducted the review come from outside the Church, "with no axe to grind, no vested interest". The review's authors are "only reflecting back what they've heard", he said.
Dr Morgan said that "it is up to the Church to act" on the report's recommendations. Lord Harries will speak to the Church in Wales's Governing Body in September, and be questioned about the report.
There are no plans yet, however, to vote on whether to implement its recommendations. But Dr Morgan said: "I sense our Governing Body has reached a point where it knows that things can't stay as they are."
The reasons for a review, listed in the report, include "the expected retirement of large numbers of clergy in the next few years, the shortage of ordinands, the joining of more parishes than can be adequately ministered to by a single priest, declining church membership, and the almost total distance of young people in Wales from the Church".
The report continues: "One overwhelming impression we have received is that the Church in Wales continues to have the structure and organisation appropriate to an established Church 100 years or so ago, but which is now stretched beyond what it can or should properly bear now."
The review team argues that the parish system, "with a single priest serving a small community is no longer sustainable. . . A change of perspective is needed: from parish to a much larger area, and from a single priest, to a team with different gifts."
The report proposes replacing parishes with larger "Ministry Areas", led by a "leadership team containing laypeople as well as clergy". Each Ministry Area might contain "25 congregations or churches", each of which should have "a designated leader and ministry team".
To address the serious shortage of young people in the Church - in 2010, just 5067 people under the age of 18 attended services on a Sunday - "there should be one trained worker appointed in each leadership team with a particular ministry to reach out to young people."
Also, in each Ministry Area there should be at least one service a week "in which the form and style of worship is such as will resonate with those unfamiliar with Church culture".
The congregations in each Ministry Area, should be self-sustaining, "responsible for raising enough money at least to cover the full costs of its own ministry team, and an appropriate proportion of diocesan costs".
Dr Morgan said: "We need to give the laity more confidence that this is their Church. They are the majority. Let's think a bit bigger; let's not be so parochially minded."