The experienced 28-year-old was voted Welling United’s player of the year for 2016/17 before leaving the Park View Road club earlier this month.
Prior to joining the Wings, Lewington, who will compete with Mitch Walker for the number one shirt at Crabble, had a brief spell playing for Margate in National League South in 2016 after having his contract terminated by mutual consent at League One side Colchester United in the summer of 2015.
He had signed for Colchester, where he made two appearances, after making 143 appearances for then-League Two club Dagenham & Redbridge.
Lewington started his career in the youth ranks at Charlton Athletic and also had stints with Dulwich Hamlet, Fisher Athletic, Sittingbourne and Leatherhead.