The soft gamma-ray repeater Swift J1555.2-5402 was discovered by means of a 12-ms duration short burst detected with Swift BAT on 2021 June 3. Then 1.6 hours after the first burst detection, NICER started daily monitoring of this X-ray source for a month. The absorbed 2-10 keV flux stays nearly constant at around 4e-11 erg/s/cm2 during the monitoring timespan, showing only a slight gradual decline. A 3.86-s periodicity is detected, and the time derivative of this period is measured to be 3.05(7)e-11 s/s. The soft X-ray pulse shows a single sinusoidal shape with a root-mean-square pulsed fraction that increases as a function of energy from 15% at 1.5 keV to 39% at 7 keV. The equatorial surface magnetic field, characteristic age, and spin-down luminosity are derived under the dipole field approximation to be 3.5e+14 G, 2.0 kyr, and 2.1e+34 erg/s, respectively. An absorbed blackbody with a temperature of 1.1 keV approximates the soft X-ray spectrum. Assuming a source distance of 10 kpc, the peak X-ray luminosity is ~8.5e+35 erg/s in the 2--10 keV band. During the period of observations, we detect 5 and 37 short bursts with Swift/BAT and NICER, respectively. Based on these observational properties, especially the inferred strong magnetic field, this new source is classified as a magnetar. We also coordinated hard X-ray and radio observations with NuSTAR, DSN, and VERA. A hard X-ray power-law component that extends up to at least 40 keV is detected at 3-sigma significance. The 10-60 keV flux, which is dominated by the power-law component, is ~9e-12 erg/s/cm2 with a photon index of ~1.2. The pulsed fraction has a sharp cutoff above 10 keV, down to ~10% in the hard-tail component band. No radio pulsations are detected during the DSN nor VERA observations. We place 7{sigma} upper limits of 0.043mJy and 0.026 mJy on the flux density at S-band and X-band, respectively.
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