There is much evidence that eukaryotes have evolved from prokaryotic cells.
It is thought that prokaryotes developed an endomembrane system by engulfing smaller specialised cells in a phagocytic manner. By engulfing an autotrophic prokaryote which harnessed light energy, a second membrane was created around it, creating the first chloroplast. The mitochondria, another double-membrane-bound organelle would have been a heterotrophic prokaryote capable of aerobic respiration. This theory is supported by the double membranes found, as well as the different composition of the inner and outer membranes of each. It is also supported by the fact that the inner membranes have a similar composition to that of prokaryotes. Additionally, each of these organelles contain their own circular DNA and are able to self replicate by a process similar to binary fission.
It is thought that the membrane infolded, much in the same way vesicles are formed, to create membrane bound organelles. Thus resulting in the golgi apparatus, ER, and vacuoles.
Further evidence includes the fact that the oldest fossils are of prokaryotes and that prokaryotes are more simple, whilst eukaryotes are specialised.