The upgraded CERN LHC for high luminosity (HL-LHC) will deliver unprecedented instantaneous luminosities to the detectors which, together with an average of up to 200 simultaneous interactions per bunch crossing, require major upgrades of the CMS electromagnetic calorimeter (ECAL). While a new detector will be installed in the endcap regions, the ECAL barrel lead tungstate crystals and photodetectors are expected to sustain the new conditions. However, a completely new and upgraded readout and trigger electronic system will be installed to cope with the challenging HL-LHC conditions. Each of the 61,200 ECAL barrel crystals will be read out by two custom ASICs providing signal amplification with two gains, ADC with 160 MHz sampling rate, and lossless data compression for the transmission of all channel data to the off-detector electronics. Trigger primitives generation by updated reconstruction algorithms as well as data acquisition will be implemented on powerful FPGAs as a part of the off-detector electronics. The upgrade of the ECAL electronics will maintain the excellent energy resolution of the current detector and, in addition, greatly improve the time resolution of electrons and photons above 10 GeV, down to a few tens of picoseconds. This paper presents the design of the individual components of the upgraded ECAL barrel detector, and results of energy linearity and time resolution measurements with a readout prototype system in a recent test beam campaign at the CERN Super Proton Synchrotron.