The one-cap All Whites international attracted interest from English scouts during his time in the A-League.
Wellington Phoenix head coach Chris Greenacre acknowledged the difficulty of retaining such talent, stating: "I'm disappointed because I want to work with the best players and Luke's one of the best prospects in New Zealand.
As a result, we were keen to extend his contract, but I can understand how a move to England is difficult to resist for a young player."
Portsmouth continue to fine-tune their squad ahead of the upcoming Championship season.
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Captain Marlon Pack traveled with the team to Germany following knee surgery, although he was not included in the active 23-man matchday roster.
