We report on a two-arm hybrid high power laser system (HPLS) able to deliver 2×10 PW femtosecond pulses, developed at the Bucharest-Magurele Extreme Light Infrastructure – Nuclear Physics facility. A hybrid Ti:sapphire chirped pulse amplifier (CPA)/BBO crystals picosecond optical parametric CPA (OPCPA) Front-End, with a crossed polarized wave filter (XPW) in between these stages, has been developed to produce 10 mJ laser pulse energy, at 10 Hz repetition rate, with more than 70 nm spectral bandwidth and high intensity contrast, in the range of 1013:1. High energy Ti:sapphire amplifier stages of both arms were seeded from this common Front-End. The final booster amplifier, equipped with a 200 mm diameter Ti:sapphire crystal, has been pumped by six 100 J nanosecond frequency doubled Nd:glass lasers, at 1 pulse/minute repetition rate, to deliver more than 300 J output energy. Considering the 10 PW compressor transmission efficiency of 74% and a compressed pulse duration of 22.7 fs, obtained at attenuated input energy level, we demonstrated that the dual-arm HPLS has the capacity to generate 10 PW peak power femtosecond pulses. The reported results represent the cornerstone of the ELI-NP 2×10 PW femtosecond laser facility, devoted to fundamental and applied nuclear physics research.