Mohammed Rehman, 25, who used the Twitter name “Silent Bomber” and asked users whether he should bomb a shopping centre or the London Underground train network, will serve a minimum of 27 years.
Judge Jeremy Baker ruled that his wife Sana Ahmed Khan, 24, must serve a minimum of 25 years after being found guilty on Tuesday.
Rehman was arrested in May after posting a tweet saying: “Westfield shopping centre or London underground? Any advice would be greatly appreciated.”
The tweet linked to an al-Qaeda statement about the July 2005 bombings in which four suicide bombers targeted London’s transport system, killing 52 people.
The couple were accused of planning their attack for around May 28.
Police seized more than 10kg of urea nitrate, which can be used to manufacture a large bomb, from their house.
Rehman also filmed himself testing explosives in the couple’s back garden.
Rehman was found guilty of creating the bomb, while his wife funded the project and bought the chemicals, the Crown Prosecution Service said.
Their bomb “would have caused multiple fatalities” if it had been detonated on the London Underground, it said.
“The intention to carry out some form of terrorism attack was clear,” Susan Hemming, head of the CPS counter terrorism division, said following the verdict.
“The pair had been very close to carrying out an attack. All they required was to purchase the chemicals to make a detonator.”