How and why is Subaru connected to the Witch (Satella)? All throughout the series, specifically, within the second Arc of the story, there are references to Subaru smelling like the Witch's Scent, Giving us the knowledge that he is Definitely connected to her.

Why is this? It's well known that Subaru was pulled from modern day Japan into this Fantasy world, as well as that he has the ability "Return to Death" In which he has the ability to Respawn.

These things most likely have things in common with his relations to the witch, though... What exactly is the relationship? How are they connected?
Satella The Jealous Witch is in love with Subaru. Why though is not known to the current arc of the latest source arc 6 (web) may change in the official version (Published book).  

The first time we supposed to see her was supposed to be in the current anime arc which is arc 3 it is not shown during the anime but every time Subaru dies he is transported (symbolizes by the arm grabbing him) to a new timeline while that happen he is transported first to a void places (for depiction look at opening 1 where the places is covered with smokes symbolizing the witches miasma which may explain why the smell grew thicker everytime he re-spawn). 

He saw an image of a girl which became clearer every loop. not only thus images pop up the more significant changes that you would observe in the anime (if they didn't cut it) he will hear the whisper of Satella saying 'I Love You' in every attempt of a reveal.(episode 20)

The fact that he say 'I love Emilia' during the Rem scene will put on perspective why Emilia was killed during his attempt to reveal the power