He won the 3000 metres title at the 2001 World Youth Championships in Athletics and stepped up a level to take the silver medal over 5000 metres at the 2002 World Junior Championships in Athletics the following year. Turning to senior competition, he was the runner-up in the 5000 m behind Hailu Mekonnen at the 2003 Afro-Asian Games and went on to claim the bronze medal in the 3000 m at the 2004 IAAF World Indoor Championships. He competed in that event twice at the IAAF World Athletics Final, in 2004 and 2005, but failed to win a medal on either occasion.
He made his global outdoor debut at the 2005 World Championships in Athletics, where he reached the semi-finals of the 1500 metres. Geneti ran a 3000 m best of 7:32.69 minutes at the Birmingham Indoor Grand Prix in February 2007. The following month he then made his debut at the 2007 IAAF World Cross Country Championships, where his 15th place finish was the second best performance by an Ethiopian (after Tadese Tola).
In March 2011, he won the Los Angeles Marathon, breaking the record by almost two minutes in his first marathon attempt. His time of 2:06:35 was the sixth fastest ever for a race débutante at that point. In his second race at the 2012 Dubai Marathon he ran a personal best time of 2:04:54 hours, but in one of the fastest races ever, he took third place behind Ayele Abshero and Dino Sefir. He did not return to competition until December, when he ran at the Honlulu Marathon and placed second to Wilson Kipsang.
|2001||World Youth Championships||Debrecen, Hungary||1st||3000 m|
|2002||World Junior Championships||Kingston, Jamaica||2nd||5000 m|
|2003||Afro-Asian Games||Hyderabad, India||2nd||5000 m|
|2004||World Indoor Championships||Budapest, Hungary||3rd||3000 m|
|World Athletics Final||Monte Carlo, Monaco||6th||3000 m|
|2005||World Championships||Helsinki, Finland||12th (semis)||1500 m|
|World Athletics Final||Monte Carlo, Monaco||9th||3000 m|
|2007||World Cross Country Championships||Mombasa, Kenya||15th||Senior race|
- 1500 metres - 3:33.83 (2005)
- 3000 metres - 7:32.69 (2006, indoor)
- 5000 metres - 13:00.25 (2005)
- Marathon - 2:04:54 (2012)
- Geneti Markos. IAAF. Retrieved on 2011-03-23.
- 2007 World XC Championships - Men's Race Results. IAAF. Retrieved on 2011-03-23.
- Reavis, Tony (2011-03-21). Geneti debuts with 2:06 in LA. IAAF. Retrieved on 2011-03-23.
- Butcher, Pat (2012-01-27). Abshero stuns with 2:04:23 debut, Mergia clocks 2:19:31 in Dubai. IAAF. Retrieved on 2012-02-04.
- Monti, David (2012-12-09). Kipsang and Galimova win windy Honolulu Marathon. IAAF. Retrieved on 2013-02-14.