Born in Uasin Gishu, Birech began competing in the steeplechase as a teenager and dipped under nine minutes for the 3000 metres steeplechase for the first time in 2010, recording 8:50.0 minutes in Nairobi. He made his breakthrough at international level in the 2011 season. He started with his first medal for Kenya at the 2011 African Junior Athletics Championships, where he was the silver medallist in a Kenyan 1–2 with Gilbert Kirui. His European debut resulted in a victory at the Miners Day Meeting in Velenje. He ran at his first Diamond League race soon after and his personal best time of 8:11.31 minutes ranked him thirteenth in the world that year, marking him out as one of Kenya's emerging talents. He won at the Barcelona Meeting and fifth at the DN Galan Diamond League. In his senior debut for Kenya, at the age of eighteen, he came fourth behind an Ethiopian trio in the steeplechase at the 2011 All-Africa Games. He began his 2012 season in Australia and won at the Sydney Track Classic. Another win came at the Kawasaki Super Meet, where he broke the meeting record. At the Doha Diamond League meet he set a personalbest of 8:06.72 minutes, but this was only enough for fourth in a quick race. He found himself behind Kenyan opposition on several occasions that year, coming third at the Golden Gala, fourth at the Olympic trials, Meeting Areva and Memorial Van Damme, and fifth at Herculis. He performed better towards the end of the season, placing second to Paul Kipsiele Koech at the Athletissima meet, winning at the Birmingham Grand Prix, and setting a meet record at the Hanžeković Memorial. His best run of 8:03.43 minutes ranked him fifth in the world that year, behind four other Kenyans. Birech beat Emmanuel Bett in a sprint finish at the Cross Internacional de Itálica in January 2013. He won on the track in May, improving the meet record at the Seiko Golden Grand Prix in Tokyo. On the 2012 IAAF Diamond League circuit he appeared regularly in the steeplechase but only twice made the top three A fourth place at the Kenyan trials saw him miss amajor tournament again and slipped down the end-of-year steeplechase rankings, coming ninth for 2013. He performed well in long-distance races, however, coming runner-up at the Cross Internacional de Venta de Baños and fourth in a 10K best of 29:00 minutes at the BOclassic. He had a breakthrough in the 2014 Diamond League season. After a fourth-place finish in Doha, he had back-to-back wins in Rome and at the Bislett Games, running a personal best and world-lead of 8:02.37 minutes in the latter. He was a narrow second to Koech at the IAAF World Challenge Beijing, but came out top in national competition at the Kenyan Athletics Championships. He was the world's dominant steeplechaser that year, losing only once between June and September. At the major events of the year, he was the favourite for the 2014 Commonwealth Games but was upset by fellow Kenyan Jonathan Ndiku, who beat Birech by two seconds, but he reversed that placing at the 2014 African Championships in Athletics to take the continental gold medal. On the circuit, he won the Diamond League races in Lausanne, Monaco, and Birmingham before going on to win the series final at the Memorial Van Damme, setting a new best of 7:58.41 minutes in the process. This mark made him the eleventh man to complete the distance in under eight minutes and placed him tenth on the all-time lists.
