Two-dimensional transition metal dichalcogenides provide a unique platform to study excitons in confined structures. Recently, several important aspects of excitons in these materials have been investigated in detail. However, the formation process of excitons from free carriers has yet to be understood. Here we report time-resolved measurements on the exciton formation process in monolayer samples of MoS2, MoSe2, WS2, and WSe2. The free electron-hole pairs, injected by an ultrashort laser pulse, immediately induce a transient absorption signal of a probe pulse tuned to the exciton resonance. The signal quickly drops by about a factor of two within 1 ps and is followed by a slower decay process. In contrast, when excitons are resonantly injected, the fast decay component is absent. Based both on its excitation excess energy and intensity dependence, this fast decay process is attributed to the formation of excitons from the electron-hole pairs. This interpretation is also consistent with a model that shows how free electron-hole pairs can be about twice more effective than excitons in altering the exciton absorption strength. From our measurements and analysis of our results, we determined that the exciton formation times in these monolayers to be shorter than 1 ps.