Also in the trade, the Cavaliers received guard Brandon Knight, forward Marquese Chriss and a 2019 first round pick from the Rockets.
They 31-22 Rockets are trying to move into the top four in the West over the second half of the season.
In a separate transaction, the Cavs will send Nik Stauskas and Wade Baldwin, both acquired from Portland earlier in the week in the deal that sent Rodney Hood to the Trail Blazers, to Houston. He's set to make $15.6 million next season.
In the case of Chriss, he's an expiring contract who will be a free agent this summer but will have an opportunity to show his worth while playing on the clearly rebuilding Cavaliers.
Seifert blasts Black Caps to big win
MS Dhoni was the top-scorer for India with 39 runs off 31 balls while no other batsman managed to impress much with the willow. I'd be lying if I said Baz wasn't one of my heroes growing up", Seifert later said, at his post-match press conference.
As a fun twist to this trade, the Rockets were in Sacramento to play the Kings as the trade materialized, with Shumpert down the hallway from his new teammates.
Shumpert, 28, has had a strong season for the resurgent Kings, averaging 8.9 points, 3.1 rebounds and 2.2 assists. General manager Koby Altman traded Kyle Korver for Burks and two second-round picks.
Houston will also reportedly send a protected 2019 first-round pick to the Cavaliers as part of the deal.
Knight, Chriss and the first rounder are headed to Cleveland.
The people spoke on condition of anonymity because the National Basketball Association trade call has not yet been completed.