Team GB matched their best ever medal haul at the Games with four, including gold for Lizzy Yarnold in the women's skeleton.
Eley, who was the team's flagbearer at the opening ceremony, wrote on Twitter: "Congratulations to Team GB for what has been a great team performance. Very proud to be a part of something so special.
"A massive thank you to everyone who has supported Team GB, your messages have gave us all a real boosts."
Sochi was the 29-year-old's third Olympics.