In a historically significant capacity, this is usually attributed to Eugen Sandow, who opened his first Institute of Physical Culture in London, in 1897. Resistance and weight training in order to gain strength has of course existed in various societies and periods prior to modernity. And England had gymnasiums prior to Sandow.

But in terms of modernity of bodybuilding technique and in terms of physique training for the sake of physique (i.e., pursuit of a muscular and bodily aesthetic optimum), Sandow is seen as embodying and facilitating its emergence, by combining permanent facilities for physique training offering specialised equipment with instruction and coaching on their use, and on appropriate exercise techniques and regimens.

This having said, much was not modern about Sandow's approach (or that of anyone else of the era), from the point of view of today. For example, the Bench Press had not yet been invented (though the Floor Press does date to Sandow's era). This difference in available equipment and technique resulted in now little-seen lifts such as the Bent Press and the Two Hands Anyhow, which owe more to the strongman tradition than to bodybuilding. Moreover, much was not modern about the goal physique of the day. For example, pectoral musculature was not actively developed (though this was also a side-effect of contemporaneous lifts).