Diseases caused by Verticillium dahliae in crops such as artichokes, sunflowers, peaches, tomatoes, peppers, olives and cotton are of varying importance in Spain. Certain composts have the capacity to suppress plant diseases while minimizing organic waste and they thus lead to a reduction in the use of fertilizers and fungicides in crop production. In this work, three growing media (grape marc compost, cork compost and a co-compost of olive mill waste and olive leaves) are compared with a standard substrate (coir fiber) in their potential to suppress Verticillium wilt in cotton (VC) and olive (VO). In addition, chemical properties (pH and electrical conductivity), enzymatic properties (beta-glucosidase, alkaline phosphatase and arylsulfatase activities) and biological properties (oxygen uptake rate: OUR) were analyzed at the start of the bioassays. The composts show different suppressive capacities. The co-compost of olive mill waste and leaves was the most suppressive against VC and VO, delaying the onset of symptoms with respect to coir fiber (by 6 and 24 days, respectively). Grape marc compost only suppressed VO. The variables that were significantly correlated with disease severity were pH, beta-glucosidase and phosphatase activities, and OUR. From the results, it was concluded that pH and beta-glucosidase activity could be considered predictors of the suppressive capacity of these composts against VC and VO. Moreover, OUR and phosphatase activity can only be considered predictors of suppressive capacity against VC and VO, respectively. All the parameters showed positive correlations with the time until the onset of symptoms of the disease. Indeed, beta-glucosidase and phosphatase activities were a best fit as a saturation-type response to the onset of symptoms of VO. This work indicates that composted olive by-products are very promising when it comes to controlling VO in organic and integrated agriculture systems. The addition of this compost to substrates used for the production of olive plants also seems recommendable.