Tighthead prop Aungier joined Connacht in the summer of 2020 and has been a regular member of the matchday squad, making 20 appearances in total.
Dowling arrived that same summer and has made a similarly positive impression at the club, playing 12 times for the province so far.
The pair have both been capped at Ireland U20 level.
Head Coach Andy Friend says: “Both Jack and Oisin are key individuals in our long-term planning, so their re-signings are hugely important and significant for us as a team. Their respective games have improved since their arrival at Connacht, and they have shown that they have what it takes to play at highest level. I’m delighted they have agreed to stay at Connacht. Our retention and recruitment is ongoing so we hope to share further news in the weeks ahead.”