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We consider the massive scalar-tensor theory in the Jordan frame $F(\Phi)=K^{2}\Phi^2$ and $U(\Phi) =(1/2)m^{2}\Phi^2$, where $F(\Phi)$ corresponds to aconstant Brans-Dicke parameter $\omega_{BD}=1/4K^2$. The constraint of theSolar System experiments is $K^2<(1/400)^2$. For dustlike matter in a spatiallyflat homogeneous isotropic universe, we reduce the equations of motion to asystem of two differential equations of first order which can be exactlysolved. We obtain simple and explicit expressions for $\frac{\Phi(z)}{\Phi(0)}$and $\frac{H(z)}{H_{0}}$ that depend only on two parameters, $K^2$ and$\Omega_{m,0}$. For $K\leq1/400$ the expansion rate $H(z)$ can be practicallysuperposed on the $\Lambda$CDM solution $H_{\Lambda}(z)$, up to high redshift$z$, but the equation of state $w_{DE}(z)$ of the dark energy is not constant:it presents a very slight crossing of the phantom divide line $w=-1$ in theneighborhood of $z=0$ and becomes very slightly positive at high redshifts.

Exact cosmological solution of a Scalar-Tensor Gravity theory compatible with the $\Lambda CDM$ model