In this study, we present a new method for forecasting arrival times and speeds of coronal mass ejections (CMEs) at any location in the inner heliosphere. This new approach enables the adoption of a highly flexible geometrical shape for the CME front with an adjustable CME angular width and an adjustable radius of curvature of its leading edge, i.e. the assumed geometry is elliptical. Using, as input, STEREO heliospheric imager (HI) observations, a new elliptic conversion (ElCon) method is introduced and combined with the use of drag-based model (DBM) fitting to quantify the deceleration or acceleration experienced by CMEs during propagation. The result is then used as input for the Ellipse Evolution Model (ElEvo). Together, ElCon, DBM fitting, and ElEvo form the novel ElEvoHI forecasting utility. To demonstrate the applicability of ElEvoHI, we forecast the arrival times and speeds of 21 CMEs remotely observed from STEREO/HI and compare them to in situ arrival times and speeds at 1 AU. Compared to the commonly used STEREO/HI fitting techniques (Fixed-$Phi$, Harmonic Mean, and Self-similar Expansion fitting), ElEvoHI improves the arrival time forecast by about 2 hours to $pm 6.5$ hours and the arrival speed forecast by $approx 250$ km s$^{-1}$ to $pm 53$ km s$^{-1}$, depending on the ellipse aspect ratio assumed. In particular, the remarkable improvement of the arrival speed prediction is potentially beneficial for predicting geomagnetic storm strength at Earth.
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