Although could not reveal what they are yet, Mr Grunenberg promised some "block- buster" exhibitions for Capital of Culture year in 2008, which will also mark Tate Liverpool's 20th birthday.
Yesterday's 10 millionth visitor was maths teacher Lilian Dunlop, 63, who came from her home in Manchester with her granddaughter Gemma Bantham to enjoy a day out in the city.
They were treated to a free meal in the cafe and a personal guided tour of the galleries.
Since the gallery opened, it has had more than 100 different exhibitions and collection displays, featuring more than 300 artists.
Among its most notable was the recent Shopping exhibition on art and consumer culture, which included a life-size replica of a Tesco supermarket.
Others were Carl Andre's infamous Equivalent VIII - universally known as the Tate Pile of Bricks - and a 40,000 strong Field by the sculptor Anthony Gormley. This involved filling one of the galleries with 40,000 pot figures which were created by the people of St Helens and modelled on the famous Chinese terracotta army.