The 27-year-old has agreed a three-year contract with Sarries and will move to Allianz Park this summer.
Clark made his Premiership debut aged 18 for Leeds in 2007 and he has won one international cap for England, which came against France in August 2015.
"Calum is a very talented player and will fit in brilliantly here," Saracens director of rugby Mark McCall said.
"He is still a player with a huge amount of potential and in our opinion he has his best years ahead of him."
Clark is Saracens' third signing for the 2017-18 season, after the announcements Wales international Liam Williams and Toulouse hooker Christopher Tolofua will join the European and Premiership champions.

Andrew Travers left the authority by "mutual agreement" after the error, officials said.
Voters were initially turned away from all 155 polling stations in the borough because their names were missing from the poll list.
An independent investigation has been launched, the council said.
In a statement issued through the council, Mr Travers said: "I have enjoyed my time at Barnet and I believe the changes we have put in place and the continued programme of growth and transformation will enable the borough to continue to thrive."
A council spokesperson said Mr Travers had "made a valuable contribution to the council during his three and half years as chief executive."
Deputy chief executive John Hooton will take over temporarily while longer term arrangements are put in place, the council said.
On election day, staff at one station said just three of the first 30 voters to show up were on the register. The rest were told to come back later.
Barnet Council apologised for the problems and later offered emergency proxy votes to residents who had been affected.
But voters in the area questioned how the result could be "fair" when not everyone was able to have their say at the ballot box.
A statement released by Mr Travers on Thursday blamed electoral registration lists for the problems.
The council's review will conclude by the end of May and the findings will be presented publicly to the General Functions Committee.
It will look at the "appropriateness" of arrangements in place for the EU Referendum in June.
A spokesman said it was currently in discussions to establish who would lead the investigation.

Japan's benchmark Nikkei index spent most of the day in negative territory to close down 0.19% at 18,264.22.
After surging almost 8% on Wednesday, the Tokyo index closed down 2.5% on Thursday  - among Asia's big losers.
Investor concern over whether or not the US Federal Reserve will raise interest rates next week has set in.
Investor sentiment has also been affected by the slowing Chinese economy, which is the world's second-biggest after the United States.
Japan's investors seem to shrug off news that Japan Post is seeking to raise as much as 1.39tn yen ($11.5bn, Â£7.4bn) in a stock market listing  - including its banking and insurance arms -  that would be one of the world's biggest this year.
The plan for the state-owned giant would be one of Japan's largest public share sales in more than 30 years.
Chinese shares traded mixed with the Shanghai Composite closing down 0.1% to 3,200.45, while Hong Kong's Hang Seng ended down 0.3% to 21,504.37.
Fresh measures from regulators to ease the volatility in the market may be working as both benchmark indexes did not move dramatically this week.
In Australia, the benchmark S&P/ASX 200 closed down 0.47% at 5,071.10 points despite gains on Wall Street overnight.
Analysts said investors there were also concerned about a possible rise in US interest rates.
After being the one bright spot in Asia yesterday, South Korea's benchmark Kospi closed down 1.06% at 1,941.37. The Bank of Korea left its benchmark rate unchanged at 1.5% on Friday.
Saracens have agreed a deal to sign flanker Calum Clark from fellow Premiership side Northampton Saints.
[NEXT_CONCEPT]
The chief executive of Barnet Council has left his role after a blunder led to some voters being turned away from polling stations on Thursday.
[NEXT_CONCEPT]
Asia's markets were mostly down in trade on Friday following a rocky week featuring particularly volatile swings in Tokyo.