Speed climber Steck and his German colleague David Göttler found the remains of Lowe and his cameraman David Bridges while preparing to climb the south face of Shishapangma in China's Himalayas.
At 8,027 metres, the peak is the world's 14th highest.
According to the Alex Lowe charitable foundation, Steck and Göttler said they had “come across the remains of two climbers still encased in blue ice but beginning to emerge from the glacier”.
Göttler telephoned Conrad Anker, the new husband of Lowe's widow and described the packs and clothing of the climbers. Anker then “concluded that the two were undoubtedly David Bridges and Alex Lowe, Jennifer's then husband”.
Anker was himself was climbing with Lowe and Bridges when they died in October 1999 but experienced only minor injuries.
Hearing about the discovery, Jenni Lowe-Anker wrote: “Alex's parents are thankful to know that their son's body has been found and that Conrad, the boys and I will make our pilgrimage to Shishapangma. It is time to put Alex to rest.”
Lowe died during an expedition in which he planned to climb Shishapangma and then ski down the mountain.
Switzerland's Ueli Steck, nicknamed the Swiss machine, in 2015 climbed to the summit of all 82 mountains in the Alps over 4,000 metres in just 62 days.
In 2013 he won an international award for ascending the south face of the 8,091m Annapurna mountain in Nepal without an oxygen tank and in a record time of 28 hours.