His replacement, according to the report, is an experienced Michigan-based CEO who joined the automaker in 2016 as the first head of its then-new Smart Mobility division. He joined the company's board of directors in 2013 and was named the chairman of Ford Smart Mobility in March 2016.
A Ford spokesman declined to discuss any management changes, but the company called a news conference for 1345 GMT (0945 ET).
Ford shares are down almost 40 percent since Fields, 56, took over three years ago, at the peak of the USA auto industry's recovery.
Bill Ford and Ford's Board of Directors thanked Fields for his significant contributions to the company. Toyota says profits will fall two years in a row.
GM is gearing up an "onslaught" of trucks for the North American market, the automaker's President Dan Ammann has announced, including a new generation of the Chevrolet Silverado large pickup truck that competes with Ford's primary profit machine, the F-series line of trucks.
On Friday, Silicon Valley electric vehicle maker Tesla Inc was valued at $51 billion, more than Ford's $43 billion. Moreover, with Google and Apple too already in this space, Fields could hardly justify Ford's position and how it plans to create profits. He is credited with transforming that company, in part by predicting the shift away from cubicles and into open office plans.
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Mr Fields began the task of Ford's transition from a traditional automaker to a "mobility" company, laying out plans to build autonomous vehicles and explore new services such as ride-hailing and car-sharing.
Hackett will have to placate investors anxious about Ford's sliding US market share and product decisions.
Nevertheless, Ford's profits for the first quarter fell $1.5 billion (1.3 billion euros) to $2 billion in its automotive segment, while it lost market share in the U.S. to General Motors (GM) - Ford's rival which posted rising profits that beat expectations.
Ford's auto sales are down 25 per cent this year - far more than the overall industry decline in the vehicle segment - and it is making little, if any, money on the cars it does sell. Ford continues to make small cars even though they're unprofitable and not in demand as buyers around the world gravitate to SUVs.
In an interview with The Wall Street Journal previous year, Mr. Hackett said he wasn't interested in being a CEO again but was interested in helping Mr. Fields think through tough challenges. James Farley, who runs Ford's European unit, has been appointed to oversee worldwide sales and marketing. Joe Hinrichs, president of Ford's Americas division, will oversee global product development, manufacturing and quality.