The 19-year-old centre-half, who was on the bench in the Premier League at Brighton on the opening day and for last night's game against West Ham, joins the Daggers ahead of their home fixture against AFC Fylde.
Last season Francis-Clarke enjoyed a fine spell on loan at St Albans City, helping the Saints to the National League South play-off final.
Town boss Rob Edwards said: “We feel Aidan has a very bright future at the club and I’m delighted he has signed a new contract. He’s a powerful, young defender who is going to get great experience at Dagenham.”
Development squad coach Adrian Forbes said: “It’s been an absolute pleasure to work with Aidan and it’s great to see that his work ethic and dedication is paying off with a new contract and the involvement he has had in and around the first tea squad this summer.
“From an Academy point of view with Joe Johnson also involved in the first team it is great to see what we are doing things right.
“Aidan deserved this but he knows it’s the first step in a long journey and it is also a message to the rest of his teammates in the 21s that there is no glass ceiling.”
Good luck with the Daggers, Aidan!