The Rays and Pirates have not announced the deal.
Archer, 29, had a 4.31 ERA and a 3-5 record in 17 starts this season for the Rays. The right-hander posted a 10-12 record with a 4.07 ERA in 2017, making the All-Star team for the second time in his career.
Meadows was the No. 9 overall pick in the 2013 MLB June Amateur Draft. The 23-year-old outfielder hit .292 with five home runs and 13 RBIs in 49 games this season for Pittsburgh. He also hit .279 with two home runs and 21 RBIs in 42 games this year in Triple-A.
Glasnow, 24, had a 4.34 ERA and a 1-2 record in 34 games this year for the Pirates.
Archer has a $6.4 million salary this season and is due $7.6 million in 2018. He is under team control through 2021. Archer has a $9 million team option in 2020 and an $11 million option in 2021, with buyouts of $1.75 million and $250,000, respectively.