The 47-year-old Lowe stalwart will bow out during the next few months, ending a professional relationship with Jerry Judge, the worldwide chief executive, that stretches back more than 25 years.
He will not be directly replaced. Instead, Ian Creasey, the president of the Asia-Pacific region, will move to London in January to take on the previously unfilled role of regional president for Europe, the Middle East and Africa.
As a result, Judge will take a more "hands-on" role in adapting and streamlining the network to meet changing client demands.
Lindsay's departure marks a further diminishing of the Lowe "old guard".
In June Paul Hammersley, the British-born chief executive of Lowe in New York, resigned after a power struggle and in September the group's founder, Sir Frank Lowe, announced his retirement.
Lindsay, who led last year's successful pitch by Lowe for Electrolux's $50 million pan-European and North American accounts, is thought to have grown increasingly frustrated at the management of Lowe's relationship with its Interpublic parent.
"After nearly 25 years in the ad business, 12 of which have been at Lowe, I've reached a point in my life where I'd simply like to be free to explore other opportunities," Lindsay said.
Judge said Lindsay wanted "to take a bit of a breather".
"We were looking at the modernisation of the network but as we were drawing up a strategy Tim decided it was time to re-evaluate his life," he said.
The resignation of Lindsay, who has previously rejected offers to work with Lowe in the US, has sparked speculation that he may do a start-up or seek a London-based European network role.