The gold miner said Sokalsky will be replaced by senior executive vice-president Kelvin Dushnisky and executive vice-president Jim Gowans, who will serve as co-presidents of the company.
The move comes just months after Thornton took over as chairman of the gold miner from founder Peter Munk.
"These structural changes put an even greater emphasis on operational excellence and will accelerate our portfolio optimization and cost-reduction initiatives, while fostering a partnership culture both inside the company and externally," Thornton said in a statement.
Other changes announced Wednesday included appointing chief financial officer Ammar Al-Joundi to the additional role of senior executive vice-president to work on the company's strategic initiatives.
CIBC analyst Alec Kodatsky said the responsibilities for strategic and financial initiatives will now fall more squarely on Thornton and Al-Joundi.
"We see these moves as a reorganization supporting the existing direction rather than signalling a broader strategic retooling," Kodatsky wrote in a note to clients.
Thornton, a former president of Goldman Sachs, joined the gold miner as a director in 2012 and was touted by Munk as the type of executive needed to take Barrick to the next level.
Munk pointed to Thornton's deep connections with China as a key asset for the company as it looks to grow.
Sokalsky has guided Barrick through a difficult period since replacing Aaron Regent two years ago and working to cut costs and improve the company's balance sheet.
However, under his watch, Barrick's share price has been cut in half and the company has taken billions in impairment charges as the price of gold has fallen.
Barrick stopped work at its Pascua-Lama project in South America last year after massive cost overruns and a court ruling that put construction on hold until it completes work to protect water systems as part of its environmental commitments.
The company has also sold what it deemed non-core operations in recent months and worked to reduce its debt with a near $3-billion stock offering late last year that was used to repay debt.
Sokalsky said Wednesday that it was time for the next phase of the company's development.
"I believe our new management structure will allow Barrick to address successfully the key challenges facing the mining industry today and, in turn, will position the company to deliver superior returns to its shareholders in the future," he said in a statement.
The changes will take effect on Sept. 15, with Sokalsky helping with the transition process.
Barrick also announced Wednesday the appointment of senior vice-president of human resources Darian Rich to the newly created role of executive vice-president of talent management, intended to retain and develop future employees.