Pillans, who will join the club in October on an ancestral visa, which means that he will not be classed as an overseas player, qualifies for England in 2023.
He started his seven-year residential qualification when he signed for Surrey in 2016, where he is currently in the last year of his contract.
“As soon as I qualify for England, I want to be up to that standard,” said Pillans, who revealed that his move to Emerald Headingley came “out of the blue”.
“That’s a long-term goal, though. My number one objective is just to improve my game as much as I can and be the best cricketer that I can be.
“I’m coming into another talented changing room, so hopefully I can continue to learn and add to the party.”
Pillans has found chances limited at Surrey, who recently took Liam Plunkett in the other direction on a three-year contract.
Tall and pacy, Pillans has taken 129 wickets in 40 first-class games at an average of 27.29, and Yorkshire detect a player with potential.
“Mat has been at Surrey for a couple of years now and he’s not had a huge amount of opportunity in the first team, so he’s looking to progress his career,” said Martyn Moxon, Yorkshire’s director of cricket.
“We’re obviously looking for that continuity of availability as well, and he fits the bill for us.
“He’s a bowler who has pace, and we’re looking forward to having him on board.
“He’s a different type of bowler to what we’ve already got, and although we’ve got a strong seam bowling squad, it’s nice, too, to have a bit of variety.
“Mat gives us something that we haven’t currently got,” he added.
Sussex regained second spot in Division Two of the County Championship after completing a comprehensive 243-run win over Derbyshire at Hove.
It was a convincing victory for Sussex after Derbyshire, who had batted so resolutely to almost match them in the first innings, subsided on the final day, succumbing to 161 all out.