If you're using React Native with TypeScript, here is the step-by-step solution:
1. Install react-native-svg
npm install react-native-svg
or
yarn add react-native-svg
2. Link native code
cd ios && pod install
3. Install react-native-svg-transformer
npm install --save-dev react-native-svg-transformer
or
yarn add --dev react-native-svg-transformer
4. Configure the react native packager
For React Native v0.59 or newer:
Merge the contents from your project's metro.config.js file with this config (create the file if it does not exist already).
const { getDefaultConfig } = require("metro-config");
module.exports = (async () => {
  const {
    resolver: { sourceExts, assetExts }
  } = await getDefaultConfig();
  return {
    transformer: {
      babelTransformerPath: require.resolve("react-native-svg-transformer")
    },
    resolver: {
      assetExts: assetExts.filter(ext => ext !== "svg"),
      sourceExts: [...sourceExts, "svg"]
    }
  };
})();
This is how my merged metro.config.js looks like:
const { getDefaultConfig } = require('metro-config')
module.exports = (async () => {
  const {
    resolver: { sourceExts, assetExts },
  } = await getDefaultConfig()
  return {
    transformer: {
      babelTransformerPath: require.resolve('react-native-svg-transformer'),
      getTransformOptions: async () => ({
        transform: {
          experimentalImportSupport: false,
          inlineRequires: true,
        },
      }),
    },
    resolver: {
      assetExts: assetExts.filter((ext) => ext !== 'svg'),
      sourceExts: [...sourceExts, 'svg'],
    },
  }
})()
5. TypeScript configuration:
If you are using TypeScript, you need to add this to your declarations.d.ts file (create one if you don't have one already):
declare module "*.svg" {
  import React from 'react';
  import { SvgProps } from "react-native-svg";
  const content: React.FC<SvgProps>;
  export default content;
}
6. Usage
...
import LogSvg from '../assets/images/Logo.svg'
export function LandingScreen(): JSX.Element {
  ...
  return (
    <View style={style.mainContainer}>
      <LogSvg style={style.logoContainer} />
    </View>
  )
}
...