The leadership change comes ahead of an operational reset for the organisation to be detailed later in the week.
"Cricket, like all national sports, has been going through a period of significant change and in recent months we have had the added uncertainty delivered by Covid-19," Eddings said in the statement.
"The entire cricket community has been affected and difficult decisions have been and will continue to be necessary to ensure that cricket at every level is in the best shape it can be now and in the future."
Eddings thanked Roberts for his service to cricket during his eight years at CA, initially as a board member and more recently as Chief Executive.
"Kevin has worked tirelessly since taking on the role in difficult circumstances in 2018, and particularly during the challenges of the past few months," Eddings said.
"He is a man of principle who has always put the best interests of cricket first. We wish him all the best for his future."
Roberts, who had been appointed on a three-year term to replace James Sutherland in October 2018, leaves his post after just 20 months at the helm. He had taken over when Australian cricket was still grappling with the aftermath of the ball-tampering scandal in South Africa in 2018.
The 47-year-old was contracted until the end of 2021 but has fallen out of favour with the CA board. Roberts was among the first to say that the fate of the T20 World Cup in October-November is uncertain due to the pandemic, leading to intense speculation on whether the event will go ahead.
However, the ICC has held back on taking a final call and the chances of the tournament happening have increased because of Australia's success in flattening the infection curve.
Roberts said: "It's been a privilege to lead and serve the sport I love as CEO of Cricket Australia... I'm proud of what we've achieved together. As a lifelong and passionate member of the cricket community, I look forward to seeing the game thrive into the future."
The English-born Hockley oversaw the successful women's T20 World Cup in February and March that culminated with Australia's win in front of 86,174 fans at the MCG on March 8, shortly before the Covid-19 pandemic brought world cricket to a halt.
Hockley was previously CA's head of commercial projects between 2015 and 2017 before taking on the T20 World Cup role. He previously worked on the 2015 men's ODI World Cup in Australia and spent six years with the London Olympics organising committee before that.
Cricket Australia has been at the receiving end over after its financial issues came to light in the wake of coronavirus outbreak.
CA has faced stiff opposition from The Australian Players' Association and a few state bodies over its cost-cutting and financial projections during the health crisis.
The body, which stood down more than 200 staff on 20 per cent pay until June end, secured a loan of $50 million last month to cover the losses if India doesn't tour Australia in the summer.
Business Standard has always strived hard to provide up-to-date information and commentary on developments that are of interest to you and have wider political and economic implications for the country and the world. Your encouragement and constant feedback on how to improve our offering have only made our resolve and commitment to these ideals stronger. Even during these difficult times arising out of Covid-19, we continue to remain committed to keeping you informed and updated with credible news, authoritative views and incisive commentary on topical issues of relevance.
We, however, have a request.
As we battle the economic impact of the pandemic, we need your support even more, so that we can continue to offer you more quality content. Our subscription model has seen an encouraging response from many of you, who have subscribed to our online content. More subscription to our online content can only help us achieve the goals of offering you even better and more relevant content. We believe in free, fair and credible journalism. Your support through more subscriptions can help us practise the journalism to which we are committed.
Support quality journalism and subscribe to Business Standard.