We study the doubly charmed tetraquark state $T_{cc}^+$ by the HAL QCD method applied to the $D^*D$ system in $(2+1)$ flavor lattice QCD at nearly physical pion mass, $m_¥pi= 146$ MeV.
We obtain the attractive potential at all distances in the $S$-wave of the isoscalar $D^* D$ system, whose long distance behavior is well described by the two-pion exchange (TPE), and it generates a virtual pole near $D^* D$ threshold with a pole position $E_{¥rm pole} = -59 (^{+53}_{-99}) (^{+2}_{-67})$ keV and an inverse scattering length $1/a_0=0.05(5)(^{+2}_{-2})$ fm$^{-1}$.
The virtual pole turns into a loosely bound state pole if the pion mass in the TPE potential is extrapolated to the physical value, $m_¥pi =135$ MeV.
The potential at the physical pion mass is shown to give a semi-quantitative description of the $D^0 D^0¥pi^+$ mass spectrum at the LHCb.