* Hochtief sells airports to Canada's PSP Investment
* Deal retroactively takes effect Jan. 1
* Hochtief sees no one-off impact on earnings
* Shares gain 4.4 percent
FRANKFURT, May 7 (Reuters) - Hochtief said it sold its airports unit to Canada's Public Sector Pension Investment Board for 1.1 billion euros ($1.4 billion), to help fund a shift towards ground transportation and energy infrastructure.
The division has holdings in airports in Budapest, Duesseldorf, Hamburg, Sydney and Tirana, said the German builder, which is controlled by Spain's ACS.
It also sold Athens Airport as part of the transaction, which will take retroactive effect from Jan. 1 this year, even though it had previously taken that hub out of the bundle, citing economic troubles in Greece.
Hochtief Chief Executive Marcelino Fernandez Verdes, who took the top job in November, is leading a drive to shed airports and real estate development businesses to cut the company's debt while making it a leading global infrastructure provider.
Relief over the end of more than three years of unsuccessful attempts to divest the unit boosted Hochtief shares, which were up 4.4 percent at 0721 GMT.
Hochtief had halted the sale early last year when it was unable to fetch a price of 1.5 billion euros ($2 billion), but later revived its efforts.
"The transaction is the result of a very competitive tendering process. We will use the released funds as planned to reduce debt and to invest in the operating infrastructure business," said CEO Verdes.
Hochtief, which is due to report first-quarter results later on Tuesday, added that it expected no significant extraordinary earnings impact from the transaction.
"The fact that the airport assets are going to be disposed completely after such a long time is positive news and should outweigh possible discussions on the pricing," said DZ-Bank analyst Marc Nettelbeck.