Neurologically speaking, β-endorphin molecules (amongst other opioids) function to relieve pain or produce pleasurable feelings, thereby facilitating an individual to continue functioning in spite of injury or stress.
β-Endorphin release in response to exercise has been known and studied since the 1980s. Studies have demonstrated that serum concentrations of endogenous opioids, in particular β-endorphin, increased in response to both acute exercise and training. The notion of β-endorphin release during exercise is colloquially known in popular culture as a runner's high.
tl;dr: Yes, it has been shown that exercise can really reduce stress in the biological meaning.