The 20-year-old will be available for all forms next summer, except for any fixtures against Middlesex and can only be recalled as an injury or international replacement.
Lace made four appearances, including his first-class debut, on loan at Derbyshire in 2018, scoring 219 runs at the top of the order at an average of 27 and with a top score of 43.
A product of the Middlesex Academy, the batsman made his Second XI debut in 2015 and scored his maiden century against Worcestershire Second XI the following summer, aged just 17.
Last summer, the right-hander played six Second XI Championship matches for Middlesex, scoring 322 runs at an average of 32.20 and with a top score of 94.
Head of Cricket, Dave Houghton said: “Tom is a young lad with a good technique and he showed last season that he has the talent and potential to be a quality cricketer.
“This is a great opportunity for him to get some regular first team cricket, while giving us another option at the top of the order.
“I would like to thank Angus Fraser and Middlesex for allowing Tom to join us. He will arrive in March and be available for the entire 2019 season.”
© Cricket World 2018