Smedley was born and grew up in Normanby, near Middlesbrough, in the north-east of England. He attended St Peter's School in South Bank and St Mary's Sixth Form College before studying at Loughborough University, where he completed both a Bachelor of Science in Mathematics and Mechanical Engineering and a master's degree in Mechanical Engineering.
After university, Smedley's first engineering role was with Pilbeam Racing Designs, where he worked on suspension elements for the Peugeot 406 competing in the 1997 British Touring Car Championship. He then worked on Formula 3000 cars and Williams touring car projects before joining Jordan Grand Prix at the start of 1999.
At Jordan, Smedley initially served as a data acquisition engineer responsible for telemetry data. For the 2002 and 2003 seasons he stepped up to the role of track engineer within the team, working directly with drivers on a race-weekend basis. It was at Jordan that he first worked alongside Giancarlo Fisichella, a connection that would later prove significant.
Smedley joined Ferrari before the 2004 season, initially working within the test team. In the middle of the 2006 season he replaced Gabriele Delli Colli as the race engineer assigned to Felipe Massa. The impact was immediate: Massa's form improved markedly, his error rate dropped, and in August 2006 the Brazilian took his first Formula One pole position and his first victory at the Turkish Grand Prix.
Smedley became widely known to the public for his frank and occasionally humorous radio transmissions to Massa. At the 2009 Malaysian Grand Prix he was heard telling Massa "Felipe baby, stay cool" as the Brazilian complained about not having a clear visor for the restarted wet race — one of the more memorable radio exchanges of that era.
Following Massa's serious head injury at the 2009 Hungarian Grand Prix, Smedley continued in the race engineer role for Massa's stand-in drivers, Luca Badoer and Giancarlo Fisichella, for the remainder of that season.
Smedley was central to one of the most controversial incidents of the 2010 season. During the German Grand Prix, with Massa leading and Fernando Alonso behind him, Smedley transmitted to Massa: "Fernando is faster than you. Can you confirm you understood that message?" The instruction was widely understood as a thinly veiled team order — prohibited under the regulations at the time — to allow Alonso through to win. Massa complied, and after the pass Smedley added: "OK mate good lad, stick with him now, sorry." Ferrari were fined $100,000 for breaching team orders regulations, but the race result was allowed to stand.
Smedley remained as Massa's engineer through to the end of the 2013 season, one of the longest and most prominent driver–engineer partnerships of the era.
When Massa joined Williams for the 2014 season, Smedley followed, heading the team's trackside vehicle performance operations. He remained at Williams until the end of the 2018 season, a year after Massa had retired from Formula One.
After leaving Williams, Smedley joined the Formula One Group in a technical advisory role. By 2020 he had moved into the role of Director of Data Systems within the organization, contributing to the commercial rights holder's growing emphasis on data and analytics.
Also in 2020, Smedley founded Total Karting (initially named Electroheads Motorsport), an electric karting series designed to make motorsport more accessible and affordable for beginners.
Smedley received an honorary degree of Doctor of Professional Studies from Teesside University in 2009. In July 2015 he was awarded an honorary Doctor of Technology from Loughborough University in recognition of his contributions to Formula One and race engineering.
Smedley is married to Lucy. They are patrons of Zoe's Place Baby Hospice and supporters of the Stillbirth and Neonatal Death Society (SANDS), and have held fundraising events on Teesside following the death of their daughter Minnie in 2007.