Kamara, 25, had been without a club since leaving Huddersfield Town in the summer and has signed on a permanent deal at Holker Street.
Meanwhile Wainwright, 31, joins on a month-long loan from League Two side Morecambe to gain match fitness after missing pre-season through injury.
Both players will travel with the squad to Salisbury.
London-born Kamara, who has one cap for Sierra Leone, began his career with MK Dons, and has also played for Cardiff City and Port Vale.
Wainwright started his career at Sunderland, and has also played for Darlington, Halifax Town and Wrexham.
Source: BBC Sport
Source: BBC Sport