The song topped the UK singles charts in February 1969 and remained number one for four weeks.
It was also number one in many other countries and won the Ivor Novello award for best song composition.
He died peacefully after a six-year battle with Progressive Supranuclear Palsy, a family statement said.
The statement said his closest family were "with him to the last" and that many people would miss his songs and his music.
Where Do You Go To (My Lovely), a song about a girl born in poverty who becomes a member of the European jet-set, was replaced as number one by Marvin Gaye's I Heard it Through the Grapevine.
It was included in the compilation programme One-Hit Wonders at the BBC, which was broadcast on BBC Four last year, although Sarstedt also reached number 10 in the charts with Frozen Orange Juice in June 1969.
He wrote more than a dozen albums in a career that spanned more than 50 years, releasing his last, Restless Heart, in 2013
Born into a musical family in India, Sarstedt was one of three brothers who all enjoyed success in the UK singles chart.
His older sibling, Richard Sarstedt, who performed under the stage name Eden Kane, also topped the charts with Well I ask You in 1961, while younger brother Clive, performing under the name Robin Sarstedt, reached number three in 1976 with My Resistance is Low.
Sarstedt's music reached new audiences when Where Do You Go To (My Lovely) was included in the Wes Anderson films Hotel Chevalier and The Darjeeling Limited, which were both released in 2007.
According to his website, he retired in 2010 because of his illness - a rare, progressive neurological condition.

Michael Hoolickin, 27, suffered multiple stab wounds in a fracas between a group of men and women on 14 October in Middleton, Greater Manchester.
Timothy Deakin, 21, of Lever Street, Heywood, denied murder but was found guilty by a jury at Bolton Crown Court.
He was ordered to serve a minimum of 27 years.
Deakin was also sentenced to three years for wounding and possession of an offensive weapon in a public place, which he had also denied, and 12 months for assault, which are to be served concurrently.
The 21-year-old admitted the assault charge.
After sentencing Mr Hoolickin's family said: "Michael was much loved by all his family and friends and had his whole life ahead of him."
The family said he was taken away in "completely unnecessary circumstances".
"We cannot express how devastated we are that his life has been stolen from him.
"Today his killer has been sentenced and justice has been served."
His family added: "We can try to repair our heartache although no matter how long the sentence is, it will not bring Michael back or make our loss any easier."

Antonsson scored 22 goals in 40 league games for Kalmar after signing from Halmstads in January 2015.
The 25-year-old is Leeds head coach Garry Monk's first signing since replacing Steve Evans on 2 June.
"He scores goals, has great movement and he has the mentality to be able to adapt to this league," Monk said.
"The club has watched a lot of him, I've watched a lot of him and I felt he'd be a good fit for Leeds United."
Find all the latest football transfers on our dedicated page.
Singer-songwriter Peter Sarstedt, best known for the song Where Do You Go To (My Lovely), has died at the age of 75, his family has said.
[NEXT_CONCEPT]
A man has been given life imprisonment for murdering a man in a mass street brawl.
[NEXT_CONCEPT]
Championship club Leeds United have signed striker Marcus Antonsson from Swedish top-flight side Kalmar on a three-year deal for an undisclosed fee.