The department’s ex-permanent secretary started an employment tribunal claim against the Home Secretary last year after quitting his post in February amid allegations of her bullying behaviour.
A Cabinet Office investigation was launched in March over allegations that Ms Patel belittled colleagues and clashed with senior officials in three different departments.
Now the FDA Union have confirmed the Government has paid out, in a figure believed to reach six-figures.
In a statement, Sir Philip said: “I am pleased to say that the Government has today settled the claims that I brought against them and which were due to be heard in an employment tribunal in September.
“I have received excellent support during this process and I would like to express warm thanks to the FDA and to my legal team, Slater and Gordon and Gavin Mansfield QC.
“I also want to record my appreciation and thanks to the many individuals, known and unknown to me, who have expressed their support throughout.
“This settlement resolves my own case. The FDA is continuing to pursue in separate proceedings the wider issues that have been raised.
“I now look forward to the next stages of my career.”
Sir Philip previously accused Ms Patel of a “vicious and orchestrated” briefing campaign against him, with his union representatives saying he was claiming “constructive dismissal”.
Ms Patel has expressed concern at the “false” claims, and allies have described her as a “demanding” boss but not a bully.
She has now avoided the 10-day tribunal trial that had been due to take place in September.
In an online statement, the Government said: “The Government and Sir Philip are now pleased that a settlement has been reached to these proceedings”, adding that it “regrets the circumstances surrounding Sir Philip’s resignation”.
In a separate statement, the Home Office said: “The Government and Sir Philip’s representatives have jointly concluded that it is in both parties’ best interests to reach a settlement at this stage rather than continuing to prepare for an employment tribunal,” adding: “The Government does not accept liability in this matter and it was right that the Government defended the case.”
Last year Boris Johnson judged the ministerial code was not breached by Ms Patel amid allegations of bullying despite an inquiry into her conduct finding she had “not consistently met the high standards expected of her”.
The Prime Minister’s adviser on ministerial standards, Sir Alex Allan, resigned in response to Mr Johnson’s decision to keep Ms Patel as Home Secretary.
Ms Patel apologised for upset caused by her behaviour, saying in a statement: “It has never been my intention to cause upset to anyone.”
Normally ministers are expected to resign if they breach the code.
Sir Alex concluded Ms Patel’s behaviour – which was said to include some occasions of shouting and swearing – met the definition of bullying adopted by the civil service.
In his advice, he said: "Her approach on occasions has amounted to behaviour that can be described as bullying in terms of the impact felt by individuals. To that extent her behaviour has been in breach of the ministerial code, even if unintentionally.”