Evolution is such an amazing process, which gives rises to the current biodiversity. No wonder biologist Theodosius Dobzhansky has said, ‘Nothing in biology makes sense except in the light of evolution.’ My answer to your question is, yes, they are related. And I am going to answer you how this happens in the light of evolution.

From the phylogenetic tree of life, we can see the domain Eukaryota emerges much later than the two other prokaryotic domains. Thus, eukaryotes must have a prokaryote-like ancestor. There are two prominent features that are unique to extant eukaryotes – the presences of (1) nucleus and (2) membrane-bound organelles (mitochondria and chloroplasts are examples). From where do eukaryotes acquire these two things?

When we talk about evolution, we must not neglect the natural environment at the time. Ancient Earth had very little amount of oxygen – of course, the high-energy-making aerobic respiration is not as common as now. There were three types of single-celled prokaryotic organisms: one is a proteobacterium that can make use of oxygen to produce energy (respiration); one is a cyanobacterium that converts light energy to chemical energy (photosynthesis); the last is miserable – it has neither of these abilities. The ‘miserable’ one could be even more miserable – the cyanobacteria were producing oxygen and changing the Earth, but it could not utilize it like the proteobacteria could!

Emergence of First Eukaryote

The ‘miserable’ one now developed infoldings in cell membrane to increase its surface area to volume ratio, possibly because it increased the food intake efficiency to compensate for its lower energy conversion efficiency. The infoldings eventually separated from the cell membrane – forming an endomembrane system, enclosing the nucleoid and genetic materials. This is the first eukaryote (eu, true; karyon, nut; meanings in Greek).

Endosymbiotic Theory (or Symbiogenesis)
 
There came a very rare chance (well, but if you consider how old the Earth is, it is not surprising at all) – The eukaryote engulfed the aerobic proteobacterium, either as food or parasite, scientists are still not quite sure. Both were lucky, the engulfed bacterium avoided the eukaryote’s digestion (Phew!) and the eukaryote assimilated it as its asset to utilize oxygen (Wow!) – no longer miserable! The proteobacterium is now an endosymbiont in the eukaryotic host. This eukaryote is the ancestor of animals, fungi, and other heterotrophs (food-consuming), and the assimilated proteobacteria become the nowadays mitochondria.
 
The increasingly oxygen-rich environment selected away other eukaryotes that had not engulfed the aerobe, because clearly the endosymbiotic eukaryote accumulated energy faster and reproduced faster.
 
At another chance, some eukaryotes took a step further – acquiring the cyanobacteria as endosymbiont. How greedy! But it certainly gained the advantage to produce its own oxygen. This eukaryote is the ancestor of plants, algae, and other autotrophs (food-self-producing), and the assimilated cyanobacteria become the nowadays chloroplasts.
 
Not only does this whole process explain the emergence of eukaryotes, it also explains why we cannot find a cell that possesses chloroplasts but not mitochondria – because proteobacteria won the race!
 
Such transversion from acquisition of endosymbionts (individuals living dependently to each other) to assimilation of organelles (dependent cellular part) is first outlined by Russian botanist Konstantin Mereschkowski, as endosymbiotic theory (or symbiogenesis). Many scientists thereafter advance the theory with more evidence.
 
Evidences of Endosymbiotic Theory
 
Wait a minute! You may say. ‘How do I know this is true?’
 
This endosymbiotic process is estimated to occur around 1.5 billion years ago – it is indeed hard to prove its validity. However, there are still some traces of evidence that are detected by scientists to support this testable hypothesis.
 
First, new mitochondria and chloroplasts have their own genomes not contained in the nuclei – they govern their replication on their own. The cell division process is known as binary fission (many use it and the term ‘amitosis’ interchangeably, but amitosis usually refers to the nucleolar division not involving formation of spindle fibres, and is more frequently referred to certain eukaryotic cells) – which is used solely by prokaryotes.
 
Second, some membrane proteins and lipids are found exclusively in mitochondria, chloroplasts and prokaryotes – including transport protein porins and membrane lipid cardiolipin.
 
Third, genomic comparisons suggest a close phylogenetic relationship between these two organelles and their proposed origins (proteobacteria and cyanobacteria).
 
With more advanced microbiological and genomic studies, endosymbiosis grows from a hypothesis to a sound theory. We are now pretty sure how eukaryotes emerge – but this does not stop scientists from finding solutions of more questions. For instance, biologists utilize mitochondrial DNA to unravel the natural history, and astrobiologists use archaea to find origins of life on Earth and other planets. Scientific inquiry is growing like evolution is.