Hawke, son of former Ton favourite Warren, has accepted a soccer scholarship in the USA and had initially planned to leave Cappielow at the end of the season.
But with Colin McMenamin's arrival knocking him down the pecking order and the reserve league season coming to an end, he feels it is in his best interests to move on in order to get game time before moving to the States.
As part of David Hopkin's reserve squad, the 19-year-old was on amateur terms, meaning he was free to depart Cappielow, although the Tele understands he goes with the club's blessing.
He is now set to sign a similar amateur contract with Annan prior to their Third Division fixture against Queen's Park at Hampden tomorrow.
Hawke told the Tele: "I felt that with the reserve season about to finish and my chances of first-team football limited, it would be best to play as much as possible before moving to America.
"I'm excited about joining Annan. Their manager Jim Chapman was keen for me to sign and I'm looking forward to working with him and trying to help Annan to the play-offs.
"It was a tough decision to leave Morton. I would like to thank the fans. They have always been fantastic with me and their support really means a lot."
Hawke was signed from boys' club Linwood Rangers in October 2011 and made an immediate impression, scoring 21 goals in 18 appearances for Ton's Under-19 side.
He went on to make nine substitute appearances in Allan Moore's first team, netting twice - one of which was a last-gasp winner in a narrow victory over Cowdenbeath in November.
See the Tele next week for an exclusive interview with the teenager.