We describe a transportable optical lattice clock based on the 1S0 -> 3P0 transition of lattice-trapped 87Sr atoms with a total systematic uncertainty of 2.1 x 10^-18. The blackbody radiation shift, which is the leading systematic effect in many strontium lattice clocks, is controlled at the level of 4.0 x 10^-19, as the atoms are interrogated inside a well-characterised, cold thermal shield. Using a transportable clock laser, the clock reaches a frequency instability of about 5 x 10^-16 (tau/s)^-0.5, which enables fast reevaluations of systematic effects. By comparing this clock to the primary caesium fountain clocks CSF1 and CSF2 at Physikalisch-Technische Bundesanstalt, we measure the clock transition frequency with a fractional uncertainty of 1.9 x 10^-16, in agreement with previous results. The clock was successfully transported and operated at different locations. It holds the potential to be used for geodetic measurements with centimetre-level or better height resolution and for accurate inter-institute frequency comparisons.