The Leeds-based group said the board has started looking for a new chief executive and in the meantime non-executive chairman John Samuel has assumed the role of executive chairman.
Mr Samuel said: "The board of directors and I would like to thank Antony for his dedication and commitment to Tissue Regenix since he was appointed CEO in 2008.
"He has been a key member of the executive team. During his tenure the company has listed on the AIM market, successfully commercialised products in the US and earlier this year completed the transformational acquisition of CellRight, while continuing to pursue additional commercial opportunities. We wish him every success in his future career."
The firm said that the integration of CellRight is continuing as planned and current trading remains in line with the board's expectations.
It is thought that the group is keen to hire a chief executive with more integration experience following the CellRight acquisition.
Analyst Chris Cooper at Jefferies said: "Having completed the potentially transformative acquisition of CellRight in July we believe the board is now looking for someone with greater commercial experience and integration expertise.
"Since his appointment in 2008, Mr Odell has overseen the IPO, the launch and early ramp of key product Dermapure, the development of several other dCELL applications and the acquisition of CellRight.
"However, in recent years Tissue Regenix has missed several commercial and development targets and, with several products at a crucial stage of commercialisation and the integration of a larger, more established business ongoing, the board likely felt the role now requires a different skill set. Longer-term we believe the previous CEO of CellRight could be a suitable candidate but the board may prefer to look closer to home for now."
In interim results last month Mr Odell said the group had seen continued revenue growth and the strategy to grow DermaPure sales in the US drove revenue growth by 118 per cent in the first half of 2017.
Tissue Regenix was formed in 2006 when it was spun-out from the University of Leeds.
The company's patented decellularisation technology removes DNA and other cellular material from animal and human soft tissue leaving an a tissue scaffold which is not rejected by the patient's body and can then be used to repair diseased or worn out body parts.
The technology can be used in many critical clinical needs such as sports medicine, heart valve replacement and wound care.
In August, Tissue Regenix acquired CellRight Technologies, a biotech company that specialises in regenerative medicine and the development of innovative wound care scaffolds that encourage healing by trauma and disease.
CellRight's technology can be used in spine, trauma, general orthopaedic, foot and ankle, dental, and sports medicine surgical procedures.