Robertson-McCoy was mainly a tighthead during his time with the Auckland Blues development side as well as Northland in the ITM Cup and will arrive for pre-season in July.
The 22-year-old prop is Irish qualified through his grandfather, who hails from Armagh.
"I first saw Dominic as he came through the Auckland Schools system and played for the Blues under-18s in New Zealand," said the New Zealand-born Lam.
"He is a young prop who can play on both sides of the scrum and I believe he has huge potential.
"I know he will continue to thrive and develop in a full-time professional environment which will be very beneficial for Connacht and Irish Rugby.
"We're looking forward to getting him over for the pre-season as we build towards the start of a new season in both the PRO12 and European Champions Cup."
Connacht have already extended the contracts of JP Cooney, Shane O'Leary and Danny Qualter for the new season while back-row forward Rory Moloney has been promoted from the academy.
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