After completing studies abroad, can I apply for permanent residency or do I have to return to India in UK/Germany for a Master's/PhD?

No, you do not have to return to India right after finishing your Master's or PhD in the UK or Germany, since both countries offer structured post-study routes that let you stay and work. What you cannot do is apply for permanent residency straight out of graduation. You need to first move through a post-study work visa, land a job, and then meet a set residency duration before PR becomes possible.

Your Route To Permanent Residency In Each Country

Key Rules To Remember For Both Countries

• In the UK, your Graduate Route application must go in while your student visa is still valid and you are still on UK soil, and there is no option to extend it later.
• The UK Graduate Route itself does not count toward the 5-year ILR residency requirement, so you must switch to a Skilled Worker Visa to start that clock.
• In Germany, B1-level German proficiency on an EU Blue Card significantly speeds up your PR timeline compared to not knowing the language.

My Advice

Treat your post-study visa as a bridge, not the finish line, and start job hunting for a role that qualifies for the UK Skilled Worker Visa or a German work permit well before that bridge visa expires. If Germany is your choice and PR speed matters to you, begin learning German toward B1 level now, since it can shave years off your route to permanent settlement.