Sudhakar will take up her new position at the end of November and will take responsibility for marketing the newspaper's online version, Telegraph.co.uk.
Lastminute.com said it does not plan to replace Sudhakar in the short term. She had been responsible for all outbound customer communications and the site's customer database. This included the development of its eCRM programme and email newsletters.
She rejoined the firm last April as CRM and customer information manager, following a four-month sabbatical travelling and writing for The Guardian.
She was previously a former senior account manager at ad agency WWAV Rapp Collins North and BA senior marketing executive.
At The Telegraph, Sudhakar will report to Annelies van den Belt, the group's new-media director, who joined in May. She was previously deputy ad sales director and digital director at Times Newspapers. Her role covers The Daily Telegraph's site and overall digital strategy.
Belt's arrival followed the exit of Telegraph.co.uk's former general manager, Tim Faircliff, who was poached by Reuters to be general manager for its UK news and business information consumer products. As its first general manager, he manages Reuters news across online, mobile and iTV platforms as the media giant attempts to grow its consumer audience.
The Telegraph has an illustrious online history, becoming the first UK daily national paper to launch an online version when the Electronic Telegraph was set up in 1994.