Since the start of 2018, the Wellington-born batsman has scored 1,232 ODI runs at an average of 82.13
Middlesex have announced the signing of New Zealand batsman Ross Taylor.
The Blackcaps' leading ODI run-scorer is likely to make is debut against Surrey on April 25 and will be available for the final five Royal London One-Day Cup group matches.
If the Lord's side progress far enough in the tournament, the 35-year-old will also be available for the play-off and semi-final on May 10 and 12 respectively.
Taylor's World Cup duties will rule him out of the final if Middlesex were to reach it.
Since the start of 2018, the Wellington-born batsman has scored 1,232 ODI runs at an average of 82.13.
Middlesex's managing director of cricket, Angus Fraser, said: "The pre World Cup schedules of England and Ireland mean that Middlesex will be without Eoin Morgan and Paul Stirling for more than half of the Royal London One-Day Cup.
"Eoin and Paul are outstanding one-day cricketers and we were keen to strengthen our resources on the back of their absence during the second half of the tournament.
"To have the opportunity to fill these gaps with a player of Ross' undoubted class is a real treat for the Club.
"He is an outstanding cricketer and a cracking man, and we look forward to welcoming him to Lord's in a couple of weeks time."