Updated again Thursday morning
The Anglican Church in North America has posted this press release from Archbishop Robert Duncan.
CANA has this response from Bishop Martyn Minns Vatican Move Recognizes Reality of Anglican Divide.
Bishop Jack Iker in Fort Worth has Response to Vatican announcement of “personal ordinariates” for Anglicans available here.
Reform in the UK has Reform Initial Response To ‘Apostolic Constitution’ Announcement.
Affirming Catholicism has issued this:
Affirming Catholicism shares the desire of all Christians, and especially Catholic Christians, for the full and visible unity of the Church of Jesus Christ. We also value our Anglican tradition as one which has its own distinctive contribution to make to the life of the whole Church, a gift of the Spirit which is an important part of the richness of God’s work in the world.
We recognise that Pope Benedict’s announcement may be of great comfort to some who combine deep attachment to Anglican patterns of worship with acceptance of the claims of the Roman Catholic Church as regards doctrine and church order. We affirm, though, that there is an authentically Catholic tradition within Anglicanism which seeks unity through a process of mutual learning. In such a process, each church will have something to give and to receive at every level of its life.
It is for that unity that we continue to pray.
The Bishops of Ebbsfleet and Richborough have this statement.
The Society of the Holy Cross has issued a statement, see here, or in the comments below.
The Traditional Anglican Communion, which is probably the main beneficiary of this development, has issued this statement.