The 25-year-old, who was signed on a free transfer in 2017, joined the Baggies on a four-year deal on Saturday.
The fee is undisclosed, but it is reported to be £1.5million with significant add-ons.
Ajayi has been one of the star players at the AESSEAL New York Staidum over the last few seasons and his form in the Championship earned him a call-up to the Nigeria squad.
Following the Millers' relegation last season and the fact that he is entering the final year of his contract meant that a summer exit was always likely.
Warne says that it is a good deal all around.
“He goes, from my point of view, with a heavy heart because I lose a great player and a good person, but I can understand the pull of the Championship and West Brom,” the manager said.
“He was in the last year of his contract, so it was understandable and good business from the club to allow him to move on.
“There has been offers coming in for him in the summer from a few Championship clubs and we wanted to make sure we did the best we could for the club.
“The player was understandably attracted by the offer and it was fair business all around really, the club wanted to take the offer and we have.”
Ajayi first arrived in South Yorkshire in 2017, having barely tasted first-team football, but he proved to be an astute signing as he went on to make over 100 appearances for the Millers.
Warne saw the potential to adapt his position to a defensive midfield role and he thrived in the second tier, finishing as the club's joint top scorer last season.
“He came in as a very shy lad and was very raw,” Warne added. “He did have the attributes I like, in that, he was athletic and he wanted to learn.
“He can play in a lot of positions and it is a massive blow for all of us at the football club that he has moved on but unless you're the richest club in the country, your best players are always in danger of being picked off.”
The Millers began life without Ajayi with a 2-1 friendly win at Chesterfield on Saturday while there will be a hasty reunion as the Baggies visit on Tuesday for another friendly.