The New Zealand couple, with help from Ms Starrie's parents and a neighbour, then spent five days in temperatures reaching -25C building the structure in the Burton's back yard.
"Once I started building it, it was something I just really wanted to finish, because you can't just leave something like that unfinished" Mr Gray said.
"There was a few calculations involved, mostly regarding an estimation of how many blocks we would require, just based on it being a spherical shape."
All up, more than 500 ice blocks were used.
Mrs Burton said if Mr Gray completed the task she would let him marry her daughter.
"So I guess I've accomplished that," Mr Gray said, although he added that marriage was not part of the couple's immediate plans.
Mr Gray then posted his exploits on chat forum reddit, gaining praise from many people around the world.
Warox13 said "... this is really cool aesthetically, and you guys did an awesome job on it."
Rustoak 38 said "as an actual Eskimo from Alaska, I approve of this."
Mr Gray replied that he never imagined his story would be so popular.
"The weather channel is now coming over to have an interview and we are having an igloo party this afternoon."
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