Lindblom, 26, will join the Rangers in time for their series opener against the Mariners.
This is Lindblom's third stint with Texas. He got a no-decision in his last outing with the Rangers after giving up two runs in five innings against the A's on June 20. He is 0-2 with a 5.40 in 21 2/3 innings for the Rangers.
McClellan was 0-1 with a 7.71 ERA in seven relief appearances since his contract was purchased from Round Rock on June 9. He allowed runs in each of his final four outings with Texas. The Rangers have 10 days to trade, release or outright McClellan to the minors.