The 27-year-old ex-Manchester City trainee is the first signing made by new Moors manager Liam McDonald.
Obeng, who made his professional debut with Wrexham, was signed by Brendan Rodgers' Swansea City in January 2012.
He had loan spells at Fleetwood Town, York City, Stevenage and Newport County before being released in October after almost five years at Swansea.
Since then, Manchester-born Obeng has been on the books of both Macclesfield Town and Altrincham, for whom he made his debut in their FA Cup first-round defeat at Lincoln City.
He was then used from the bench in Saturday's National League North game at Alfreton.
His latest move allows him to step up a level to the National League, in which the Moors are 16th following Saturday's defeat at Barrow - but he will be ineligible for the FA Cup second-round tie at Luton on 3 December, having already played in the competition for Altrincham.
Solihull Moors have signed former England youth international defender Curtis Obeng from Altrincham.