In America, the first compressors I'm aware of all follow the lead of the Western Electric 110A, which showed up in 1937. It was immediately joined by the RCA 96-A, the Collins 26C, the Gates 17-B, and shortly thereafter the Wilcox 57-D in 1938.
Post-war, the Collins 26C was re-worked to be the 26W. The Gates 17-B morphed through several revisions ending with the 28-CO's exit from the market after 1949. The RCA 96-A lived on with a vastly simplified power supply as the 86-A. The WE 110A was replaced with the 1126A.
The RCA 96-A appears to be the first one using vari-mu tubes. The Gates 17-B used some vari-mu in conjunction with lightbulbs (the first professional opto-limiter?) as variable resistors in a bridge network. The WE 110A and the Collins 26C also both used bridge networks with varying network arms to achieve gain reduction. The Collins used tubes as network arms, the WE 110A appears to use Selenium rectifiers in each arm(!).
The earliest article I've seen about broadcast limiting is a DIY article in Electronics Magazine, June, 1936, which I think pre-dates commercially available products.
The earliest mention of lightbulb limiting or expansion I've seen is in Electronics Magazine, also somewhere around 1934. I'll correct when I find it again.