Cells and organelles are delimited by lipid bilayers in which high deformability is essential to many cell processes, including motility, endocytosis and cell division. Membrane tension is therefore a major regulator of the cell processes that remodel membranes, albeit one that is very hard to measure in vivo. Here we show that a planarizable push-pull fluorescent probe called FliptR (fluorescent lipid tension reporter) can monitor changes in membrane tension by changing its fluorescence lifetime as a function of the twist between its fluorescent groups. The fluorescence lifetime depends linearly on membrane tension within cells, enabling an easy quantification of membrane tension by fluorescence lifetime imaging microscopy. We further show, using model membranes, that this linear dependency between lifetime of the probe and membrane tension relies on a membrane-tension-dependent lipid phase separation. We also provide calibration curves that enable accurate measurement of membrane tension using fluorescence lifetime imaging microscopy.