Sort of. The history is a bit complex and lengthy.
Summarizing :
TCP/IP was created and initially used on ARPANET (Advanced Research Projects Agency Network). ARPA (now DARPA) was part of the Department of Defence and responsible for advanced military R&D.
ARPANET essentially became NSFNET (National Science Foundation Network, operated by the civilian National Science Foundation) in the mid-1980s. The military components of ARPANET were split off into their own network known as MILNET.
NSFNET and ARPANET were initially strictly non-commercial networks for academic and government use.
In 1990, NSF allowed Advanced Network and Services (who operated the hardware infrastructure for NSFNET's T1 backbone) to allow commercial traffic to use the NSFNET backbone under certain conditions via it's CO+RE subsidiary. This is where what we'd recognize as the modern Internet comes into being. This availability of ready-made infrastructure resulted in the rapid merging of other previous networks (University networks like UUCPNET, Merit, and BITNET, private services like FidoNet and X.25-based systems, etc.) into the Internet and the rapid expansion of the Web.
Private interests began building their own backbone links beyond the NSF's (which only connected certain major cities in the USA and a handful of other cities globally), giving wider access to the Internet. NSFNET's backbone and privately-built commercial backbone grew alongside each other for a time, but NSFNET backbone was eventually superseded by the commercial Internet and decommissioned in 1995.