Anthony arrived at Plymouth in 1623 on the ship Ann. Since he had four acres in the 1623 land division, his wife and two children probably came with him. He sold his house in Plymouth to Daniel Ray, 9 June 1630, and probably went to Scituate that year, becoming one of the earliest settlers there. He was on the 1633 list of freemen and was chosen constable for Scituate on 1 January 1633/4. He and his wife, Jane, were original members of the Reverend Lothrop's Scituate Church, and probably left Scituate with Lothrop (New England Historical and Genealogical Register 9:279) as he sold his lands in Scituate to Thomas Rawlins in 1640. He was a deputy for Scituate, 4 June 1639, and a deputy for Barnstable, 2 June 1640. His house in Scituate was on Kent Street, the sixth lot from Satuit Brook, between Elder Henry Cobb's on the north and the Meetinghouse common on the south. Also, he had eighty acres of land on Stony Cove at the North River, between that cove and Edward Foster's land on the south.

Anthony made his will 24 February 1672/3, with codicil dated 23 April 1674, sworn 4 June 1674, in which he named his wife Ann, son Samuel, daughter Desire, and other unnamed daughters.

Anthony and his first wife Jane (Mumford) Annable had at least four children, order, places, and dates of birth uncertain:

• Sarah, b. probably in England; m. Henry Ewell of Scituate, MA.
• Hannah, b. probably in England; m. in 1644 Thomas Bowman of Barnstable, MA.
• Susanna, m. in Scituate, MA, 13 May 1652, William Hatch of Scituate.
• Deborah, no other information known.
• Possible other daughter who probably died young.

Anthony and his second wife Ann (Clarke) Annable had at least three children:

• Samuel, named in his father's will.
• Ezekiel, probably died young.
• Desire, named in her father's will.