Argentina international centre Tiesi has signed a two-year extension and hooker Thompson has signed for a further year.
The pair join Scott MacLeod in committing to the Falcons after the former Scotland lock signed a one-year deal.
Newcastle director of rugby Dean Richards said: "After Scott MacLeod re-signed last night, it is great to see two more commit their futures to the club.
"Gonzalo and Matt are talented individuals and bring a wealth of experience to the table which is vital in the Aviva Premiership."
- Sports & Recreation
- Scott MacLeod
- Dean Richards