In the present work, we study the evolution of metastable and Cu-containing precursor precipitates into stable β-Mg2Si using in-situ transmission electron microscopy during continuous heating of an AA6061 aluminum alloy. The experiments indicate that the transformation into stable β-Mg2Si involves the release of Al and Cu atoms into the matrix phase combined with the rearrangement of Mg and Si at the interfaces. Nucleation of the β-Mg2Si precipitates predominantly occurs at the interface between the precursors and the aluminum matrix and at dispersoids. The term precipitate-related transformation is used to emphasize the reaction mechanism, where a new product precipitate nucleates next to a precursor and consumes it at its original location predominantly via interface diffusion. The in-situ investigations are complemented by an analysis of bulk samples and a comparison with differential scanning calorimetry measurements, which show excellent agreement.