The annual series of charity concerts - which are organised by The Who frontman Roger Daltrey and take place 25-31 March - will also see performances from Rudimental, who will be supported by Ghetts, and The Levellers.
Take That are performing at the event for the first time, while Doves - who haven't played live together since October 2010 - previously headlined in 2003.
The Script feel ''honoured'' to have been asked to perform.
They said in a statement: ''We are honoured to be asked to support the Teenage Cancer Trust at The Royal Albert Hall. The fantastic work that they been done over the years continues to pay dividends to provide specialist care to young people with cancer across the UK.''
Levellers will play a full electric set as part of their own curated show 'A Beautiful Night Out', a one-day version of their own Beautiful Days festival.
Roger is ''incredibly grateful'' to all the acts who have signed up for the shows.
He said: ''Many people will not be aware that Teenage Cancer Trust is a charity that receives no government funding and is dependent on raising money from the public to provide vital wards and nursing care which are a lifeline for young people with cancer.
''I'm incredibly grateful to all of the artists who've given up time in their busy schedules to help young people with cancer get the specialist care they deserve. Looking back, we've had so many unforgettable moments at the shows over the years and these moments are amplified by the wonderful young people with cancer I have met.
'''m consistently overwhelmed by their positivity in the face of a life changing circumstance. They are the reason we strive to make these shows the very best we can and this year will be no different.''
Tickets for the shows go on sale on Friday (07.12.18).
Teenage Cancer Trust at the Royal Albert Hall - full line up
Levellers 'A Beautiful Night Out'