Similar to British Council IELTS Scholarships India, you also have ETS TOEFL scholarships, for those who chose TOEFL over IELTS to pursue their higher education. A total of 9 scholarships will awarded by ETS to students with exceptional performance. Three of those scholarships amount to $10000 each and remaining 6 amount to $5000 each (although this may change next year).
To be eligible for these scholarships, you must be a citizen of India, have a GPA of at least 80 (or 3, on a 4 point scale), have a valid TOEFL score, get admission in any foreign institute and apply before deadlines.
While applying, you must send your TOEFL scores, an essay, official transcript apart from the filled in scholarships itself.
Selection process will also involve an Interview (via telephone or Skype, as applicable). Finally selected candidates will be called for a ceremony and the scholarships will be directly sent to the University/Institute where you were admitted.
You may download the scholarship application form from here (strike this off)
Update: Scholarships for 2011 are done and you can look forward for applying to 2012 scholarships. Till then, you can have a look at this schedule to get an idea on the deadlines that you might have to adhere to next year.