"Nevin's loss will be felt deeply by us all. We are equally saddened by the tragic deaths of his father Noel and his brother Graham.
"The thoughts of every member of the squad are with Nevin's mother Essie, and his sisters Emma and Laura. We would also like to pass on our condolences to Graham's wife and children. We wish Emma a full and speedy recovery."
The South African international spoke of the type of player and person Nevin was, the 42-times capped Ulster centre being an inspirational figure to have as a team-mate and a positive force both on and off the pitch.
"Nevin Spence was a highly skilful and gifted rugby player. He was utterly committed to Ulster and was enormously proud to represent his province.
"He was determined to be the best that he could be and I have no doubt that he would have gone on to play for Ireland on many occasions. He was the kind of player that inspired others with his attitude in training and sheer will to win in matches.
"His positive outlook on life brought a smile to people's faces. He was kind, polite, generous and courageous, and we were blessed to have him in our team
"The one comfort for us as a squad is that we have each other for support. It has been a difficult time for the players and coaches but I believe that through this tragic loss, we will have a new sense of togetherness."
Muller also gave thanks to the members of the public and the rugby community around the world who have passed on messages of sympathy to honour the passing of Nevin, Noel and Graham.
"I and the rest of the Ulster Rugby squad would like to thank the many people who have sent messages of support to the club, not only from within the province, but throughout Ireland, Europe and the world.
"It is clear from these messages that Nevin was highly regarded by players and fans of many different sports, in many different countries.
"I would like to thank the organising committee of the RaboDirect PRO12 for postponing this weekend's game with Zebre and for allowing us the space and time to begin to come to terms with Nevin's loss."
The second row added: "In the coming weeks, the Ulster Rugby team will return to the pitch. Over the course of the rest of this year and in future seasons we will experience wins and we will no doubt suffer defeats. Players will move on or retire and new players will come in and represent the province.
"But going forward, at Ulster Rugby, one thing will never change. As long as this great club exists, the person and the player, Nevin Spence, will never be forgotten."
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