Sargeant's body was found on Tuesday at an address in Connah's Quay in north Wales.
The force said the death of the 49-year-old was not being treated as suspicious, while the Press Association news agency said Sargeant was understood to have committed suicide.
The former Welsh government minister resigned on November 3 and was suspended from the Labour party after he was informed of allegations against him.
Sargeant was one of a number of British politicians to have faced allegations of misconduct in recent weeks, prompting party leaders to introduce new safeguards for parliamentary staff on Monday.
His family said he was "the glue that bound us together" and "the most kind and caring husband, father, son and friend".
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A former chemical plant worker, Sargeant was first elected to the Welsh regional government in 2003, rising through the ranks before being named cabinet secretary for communities and children in May 2016.
Labour leader Jeremy Corbyn tweeted he was "deeply shocked to hear of the terrible news about Carl Sargeant. My thoughts and profound sympathy are with his family and friends."
The National Assembly for Wales cancelled all business at the 60-seat regional government following the announcement.
"He made an enormous contribution to the development of this democratic institution," said the Assembly's presiding officer Elin Jones.
"We will all want to gather our thoughts before paying proper tribute to him over the coming days."
Family and friends gathered outside Sargeant's home in Connah's Quay on Tuesday, as a black private ambulance left the property guarded by police.
"Today I find myself in very dark days. It's such a sad loss of such a great friend of mine," Bernie Attridge told the Press Association.
"At the end of the day allegations were made, I'm a great believer you are innocent until proven guilty," he added.
Distressing allegations
Announcing his resignation on Friday, Sargeant said he found the allegations against him "shocking and distressing" and requested Labour carry out an independent investigation into the claims.
"Given the nature of the allegations, I agreed with the First Minister that it was right that I stand aside from cabinet today. I look forward to returning to government once my name has been cleared," he said in a statement posted on Twitter.
Accusations of misconduct have also been made against about a dozen MPs from the Labour Party and the ruling Conservatives, which led to the resignation last week of defence secretary Michael Fallon.
First Secretary of State Damian Green, Prime Minister Theresa May's deputy, is under investigation by the government over harassment claims, some of which date back several years.
Wider sexual assault allegations include an unnamed Labour party member being accused of rape by a prominent party activist, Bex Bailey, who said the incident took place six years ago when she was 19.
A number of people who have come forward with allegations have complained of poor reporting procedures within political parties and Westminster.
Party leaders have vowed to overhaul the system and on Monday they promised to upgrade an existing complaints hotline with a face-to-face human resources service.
The new service will be in place by the end of the month, while a new grievance procedure will be introduced next year, May told reporters on Monday after meeting with Corbyn and other leaders in parliament.
