Yes you are definitely eligible after your b.tech. Around 80% of students are engineers like you who pursue MBA degree. For eligiblity in exam you also need to have min 50% in 10th, 12th and graduation for general, OBC category and 45% for SC/ST category.

There are different exams conducted for admission in various colleges to pursue MBA degree like CAT (especially for IIMs but it's score is also valid in most of the other private b-schools also), XAT (especially for XLRI but it's score is also valid in most of the other private colleges), MAT, CMAT, CET, ATMA, GMAT  ( This exam helps you if you want to pursue MBA degree from outside India, it's score is also valid for b-school in India i.e. ISB Hyderabad )

There are also some of the top reputated colleges which conducts their own exams like IIFT for Indian Institute of foreign trade college, NMAT for Narsee Monjee, SNAP for symbiosis etc.

You need to aim for a very high percentile in order to get admission in a top reputated college with decent academic records.

All the best!!