Kingsley Burrell, 29, died from cardiac arrest after being arrested following a disturbance in Birmingham in 2011.
An inquest in 2015 found restraint had been a factor in his death. The officers have also been charged with perverting the course of justice.
Constables Paul Adey, 36, Mark Fannon, 45, and Paul Greenfield, 50, have been suspended by West Midlands Police.
The charges relate to evidence given during Mr Burrell's inquest, the force said.
More updates on this story and others in Birmingham
"After investigation by the IPCC, the matter was referred to the Director of Public Prosecutions who has authorised the charges," it said in a statement.
The officers, who are all based at the Birmingham West and Central police station, will appear at the city's magistrates court on 31 October.
Mr Burrell was arrested and sectioned after calling police claiming two men has put a gun to his head. Days later he died from after a cardiac arrest at Queen Elizabeth Hospital in Birmingham.
An initial investigation by the CPS found in July 2014 there was insufficient evidence to prosecute anyone over Mr Burrell's death.
But an inquest a year later concluded prolonged restraint and a failure to provide medical help had contributed to his death.
The CPS relaunched a second investigation after the IPCC found there was a case to answer for gross misconduct against three officers, on the grounds of honesty and integrity.
Mr Burrell's family, who have held several protests demanding answers over his death, said the decision had been "a long time coming".
"The Burrell family welcome today's decision to prosecute the three officers concerned, in the belief that they must be publicly held to account for their actions in the circumstances surrounding the death of Kingsley," it said in a statement.
"This has been a long time coming and the fight for Justice for Kingsley continues."

The number of active users on the social network reached 255 million in the first three months of 2014, up 5.8% on the previous quarter but below analysts' expectations.
Twitter also reported a net loss of $132m (Â£78m) for the latest quarter.
But it posted revenue of $250m, $226m of which came through advertising.
Despite higher user growth than the previous quarter, when Twitter saw just a 3.8% rise, Twitter's stocks fell by more than 11% in after-hours trading, sending the price below its initial public offering of $38.80 per share.
The rise in Twitter active users comes after four consecutive quarters of declining growth, but the turnaround was not strong enough to convince investors.
Twitter's chief executive Dick Costolo highlighted the company's revenue increase, and said it was "fuelled by increased engagement and user growth".
The integration of advertising management software MoPub had helped Twitter "reach more than 1bn iOS and Android users each month", he added.
Another measure of user engagement, timeline views, increased 15% in the first three months of 2014 to 157 billion.
But the number of Twitter users is still well below its most high-profile competitor, Facebook, which boasts 1.28 billion active users.
WhatsApp, the messaging app Facebook bought for $19bn, recently passed the 500 million user milestone.
Three police officers have been charged with perjury following the death of a student in custody five years ago.
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Shares in Twitter dropped to their lowest levels since the company's stock market flotation, as it reported slower than expected user growth.