Vose, 22, scored 10 goals in 28 games for the Dragons this season and has signed a two-and-a-half-year deal.
Van Veen, 24, moved to the Iron from Dutch second division side FC Oss in January 2015.
Since moving to Glanford Park, he has scored four goals in 45 matches.
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Scunthorpe United have signed Wrexham winger Dominic Vose for an undisclosed fee while striker Kevin van Veen has joined SC Cambuur Leeuwarden on loan until the end of the season.