
Miss Hungary, Edina Kulcsar, was the runner-up in the contest and Miss United States, Elizabeth Safrit, came in third as an estimated billion viewers watched the finale on television around the globe.
Priyanka Chopra was the last Indian winner of the coveted title in 2000.
21-year-old Jaipur-born Rana made it to the top 10 but failed to make it to the top five.
Rana, however, bagged the sub-title of Best Designer of the world where she was seen standing gorgeously tall in a Falguni & Shane Peacock gown. She also shared the "Beauty With A Purpose" title with Kenya, Guyana, Brazil and Indonesia.
She was amongst top five in the Beach Beauty contest.
Rana, who is an active social worker and has an NGO, performed to a bollywood song at the start of the event.
"I am extremely thankful to Miss India Organization, my family and friends for supporting me through this wonderful journey. It was a wonderful experience," Rana said after the event.
She is currently the face of FBB, Neutrogena and many more fashion brands. She has also been a showstopper for top designers and jewellery brands.
22-year-old Strauss, a medical student, beat 121 contestants across the globe to the coveted title and was presented with the sash by the outgoing Miss World, Megan Young of the Philippines.
She then sat in the winner's throne as the 2013 champion put the glittering crown on her head at the ExCeL exhibition centre in east London.
"South Africa this is for you. I think I will brace myself for what's about to happen. It's a huge responsibility," she said.
The Miss World pageant returned to the British capital city for the 2014 edition after its inception 63 years ago. The events started on November 20, culminating in the grand finale tonight.
The event this year has been overshadowed by the murder of Miss Honduras, 19-year-old Maria Jose Alvarado, who was shot dead with her sister in their homeland last month on the day she was due to travel to London.
This year's winner will travel to the violence-hit central American nation to build a school named in their honour.
Rana was leading at number one when the semi-finalists were announced but could not make it to the next stage as the judges selected the top five at the 64th annual competetion.
The 10 contestants who topped the final scoreboard were, in descending order, from India, South Africa, England, Guyana, Brazil, Hungary, Kenya, US, Mexico and Australia.
They were joined by Miss Thailand, who won the people's choice award.
The scores were then reset to zero and the judges chose Miss Hungary, Miss Australia, Miss South Africa, Miss United States and Miss England as their top five.