The Lyman alpha (Ly alpha) line of Hydrogen is a prominent feature in the spectra of star-forming galaxies, usually redshifted by a few hundreds of km s(-1) compared to the systemic redshift. This large offset hampers follow-up surveys, galaxy pair statistics, and correlations with quasar absorption lines when only Ly alpha is available. We propose diagnostics that can be used to recover the systemic redshift directly from the properties of the Ly alpha line profile. We use spectroscopic observations of Ly alpha emitters for which a precise measurement of the systemic redshift is available. Our sample contains 13 sources detected between z approximate to 3 and z approximate to 6 as part of various multi-unit spectroscopic explorer guaranteed time observations. We also include a compilation of spectroscopic Ly alpha data from the literature spanning a wide redshift range (z approximate to 0-8). First, restricting our analysis to double-peaked Ly alpha spectra, we find a tight correlation between the velocity offset of the red peak with respect to the systemic redshift, V-peak(red), and the separation of the peaks. Secondly, we find a correlation between V-peak(red) and the full width at half-maximum of the Ly alpha line. Fitting formulas to estimate systemic redshifts of galaxies with an accuracy of <= 100 km s(-1), when only the Ly alpha emission line is available, are given for the two methods.