The new museum is due to open in spring 2011
Tourism bosses have been hit with a bill of £750,000 because the new Museum of Liverpool partially blocks the view from an iconic waterfront building.
The £72m attraction on the Pier Head interrupts the view from the Port of Liverpool building - one of the city's historic "Three Graces".
A 1963 covenant states those who break the height restrictions must pay compensation to affected parties.
The museum said it had no option but to pay so the project could go ahead.
The figure was reached following discussions between National Museums of Liverpool, which runs the Museum of Liverpool, and Downing, the property company which owns the Port of Liverpool building.
The building is home to the offices of companies such as Rathbone and GHL, but workers' views of the River Mersey and the Birkenhead docks are partly blocked by the new museum, which is due to open in spring 2011.
National Museum Liverpool said: "It is not unusual for there to be ancient agreements in place on land in prominent locations.
The "Three Graces" are a famous symbol of Liverpool
"Pre-2005 we were made aware of a land covenant issue restricting the height of any development and given the scale of museum needed it was necessary to remove that restriction.
"We would rather have spent this money on the museum. But to put it in context, this amounted to around 1% of the total cost of the entire project."
A Downing spokesman said restrictive building covenants are granted and exist for a "good reason" - to protect property and those who choose to make substantial investments.
The spokesman added: "Clearly, the grade II listed Port of Liverpool Building is a centre-piece of Liverpool's waterfront and the integrity of the site needs to be considered."
National Museums Liverpool said the new X-shaped museum will reflect the city's unique geography and 800-year history of people and culture.