At this time last year Maloney was considered the front-runner for the spot, with Yachting New Zealand opting to send him to the test event in Rio last year.
But Meech produced an impressive run of results over the European regatta season to secure his first Olympic appearance.
Meech's younger sister Molly is also appearing in her first Olympics, contesting the 49erFX alongside Alex Maloney - Andy's sister.
Molly Meech was out on another race course completing their third race of the day while her brother battled it out for bronze - and her performances today ensured she is a good chance of joining her brother in the ranks of Olympic medallist. Meech and Maloney are ranked second in the high performance skiff class with one race remaining before Friday's medal race.
New Zealand have a remote chance of securing further medals in the sailing today, with Josh Junior contesting the medal race in the Finn class, while Gemma Jones and Jason Saunders are through to the decider in the Nacra 17 class.
Final standings in Laser class
1. Tom Burton (AUS) 73
2. Tonci Stipanovic (CRO) 75
3. Sam Meech (NZL) 85
4. Robert Scheidt (BRA) 89
5. Jean Baptiste Bernaz (FRA) 86
6. Nick Thompson (GBR) 103
7. Pavlos Kontides (CYP) 104
8. Juan Ignacio Maegli Aguero (GUA) 117
9. Rutger van Schaardenburg )NED) 118
10. Julio Alsogaray (ARG) 129