Azam, 25, joins the Blues from Ashton United, who he joined in July 2021.
A former Burnley U18's player, Azam has featured for various clubs such as Nelson FC, Chorley and Colne.
The right-back made 41 appearances for Colne and scored 3 goals.
Joining him at Shawbridge is Lewis Richmond.
Richmond, who started in Burnley's Academy, has been playing his football in the United States for college football team Wayland Baptist University in Texas.
The pair featured in Clitheroe's pre-season fixtures.
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