Dr. Tavaré has received several awards during his career. Fellowships and elections to learned societies are listed below.
- Honorary degree of Doctor of Science from the University of St Andrews (2023)
- Elected Honorary Fellow of Christ’s College, Cambridge (2020)
- Elected International Member of the National Academy of Sciences (2018)
- Elected Fellow, American Mathematical Society (Class of 2018)
- Doctor of Science honoris causa, University of Sheffield (2017)
- Elected member of EMBO (2015)
- President, London Mathematical Society (Nov 2015-Nov 2017), President-Designate (Nov 2014-Nov 2015)
- Doctor of Technology honoris causa, Chalmers University (Sweden, 2014)
- Elected Fellow, Royal Society (FRS) (2011)
- Fellow by nomination, Institute of Mathematics and its Applications (FIMA) (2010)
- Fellow by nomination, Royal Society of Biology (FRSB) (2009)
- Elected Fellow, Academy of Medical Sciences (FMedSci) (2009), Council (2011-2014)
- Elected Fellow, American Statistical Association - 2004
- Elected Fellow, American Association for the Advancement of Science (1998)
- Elected Fellow, Institute of Mathematical Statistics (1992), Council (2016-2019)
- Fellow, Royal Statistical Society (1974)
- Professorial Fellow of Christ College (Cambridge, 2003-2019)
- Chalmers Jubilee Professor, Chalmers University (Sweden, June-Dec 2010)
- Royal Society/Wolfson Research Merit Award (2003-2009)
- G. C. Steward Visiting Fellowship in Mathematics, Gonville and Caius College (Cambridge, Jan-Jul 2003)