Gradients of signaling proteins are essential for inducing tissue morphogenesis. However, mechanisms of gradient formation remain controversial. Here we characterized the distribution of fluorescently-tagged signaling proteins, FGF and FGFR, expressed at physiological levels from the genomic knock-in alleles in Drosophila. FGF produced in the larval wing imaginal-disc moves to the air-sac-primordium (ASP) through FGFR-containing cytonemes that extend from the ASP to contact the wing-disc source. The number of FGF-receiving cytonemes extended by ASP cells decreases gradually with increasing distance from the source, generating a recipient-specific FGF gradient. Acting as a morphogen in the ASP, FGF activates concentration-dependent gene expression, inducing pointed-P1 at higher and cut at lower levels. The transcription-factors Pointed-P1 and Cut antagonize each other and differentially regulate formation of FGFR-containing cytonemes, creating regions with higher-to-lower numbers of FGF-receiving cytonemes. These results reveal a robust mechanism where morphogens self-generate precise tissue-specific gradient contours through feedback regulation of cytoneme-mediated dispersion.