The 31-year-old custodian was released by Leeds at the end of the season and Robins boss Danny Wilson has moved swiftly to secure his services.
Wilson told the club's official website: "He has great experience - in the Coca-Cola Championship and League One - and
I am delighted to have him here.
"He will provide the keepers with good competition next season and is loud, has a big frame and will do a good job for Swindon Town."
Lucas passed a medical at the County Ground on Tuesday and will official become a Swindon player on July 1.