The 18-year-old, on loan from struggling Kidderminster Harriers after joining the National League club in August following four years with West Bromwich Albion, signed for Kitching on Wednesday.
His signing ended speculation in the media that had forced the First Division South club to issue a statement on Twitter on Tuesday insisting they were still in talks with the player following his release from Aggborough.
Cater rounded off his loan spell at Marston Road last Saturday with two goals as a second half substitute in a 3-0 win over Carlton Town to send Rangers 12 points clear at the top of the table.
Kitching, who wasted no time in snapping up the youngster who has netted three goals so far in nine appearances, said: "He's got quality in abundance, good feet and can finish. He gives us a threat and can get in behind defences."
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