gradlewが存在するディレクトリで次のコマンドを叩く

./gradlew dependencies --configuration compile

依存関係がツリー上に列挙され組み込みtomcatは手元の環境では8.5.11ということがわかる。

dependencies

------------------------------------------------------------
Root project
------------------------------------------------------------

compile - Dependencies for source set 'main' (deprecated, use 'implementation ' instead).
+--- org.springframework.boot:spring-boot-starter-web: -> 1.5.2.RELEASE
|    +--- org.springframework.boot:spring-boot-starter:1.5.2.RELEASE
|    |    +--- org.springframework.boot:spring-boot:1.5.2.RELEASE
|    |    |    +--- org.springframework:spring-core:4.3.7.RELEASE
|    |    |    \--- org.springframework:spring-context:4.3.7.RELEASE
|    |    |         +--- org.springframework:spring-aop:4.3.7.RELEASE
|    |    |         |    +--- org.springframework:spring-beans:4.3.7.RELEASE
|    |    |         |    |    \--- org.springframework:spring-core:4.3.7.RELEASE
|    |    |         |    \--- org.springframework:spring-core:4.3.7.RELEASE
|    |    |         +--- org.springframework:spring-beans:4.3.7.RELEASE (*)
|    |    |         +--- org.springframework:spring-core:4.3.7.RELEASE
|    |    |         \--- org.springframework:spring-expression:4.3.7.RELEASE
|    |    |              \--- org.springframework:spring-core:4.3.7.RELEASE
|    |    +--- org.springframework.boot:spring-boot-autoconfigure:1.5.2.RELEASE
|    |    |    \--- org.springframework.boot:spring-boot:1.5.2.RELEASE (*)
|    |    +--- org.springframework.boot:spring-boot-starter-logging:1.5.2.RELEASE
|    |    |    +--- ch.qos.logback:logback-classic:1.1.11
|    |    |    |    +--- ch.qos.logback:logback-core:1.1.11
|    |    |    |    \--- org.slf4j:slf4j-api:1.7.22 -> 1.7.24
|    |    |    +--- org.slf4j:jcl-over-slf4j:1.7.24
|    |    |    |    \--- org.slf4j:slf4j-api:1.7.24
|    |    |    +--- org.slf4j:jul-to-slf4j:1.7.24
|    |    |    |    \--- org.slf4j:slf4j-api:1.7.24
|    |    |    \--- org.slf4j:log4j-over-slf4j:1.7.24
|    |    |         \--- org.slf4j:slf4j-api:1.7.24
|    |    +--- org.springframework:spring-core:4.3.7.RELEASE
|    |    \--- org.yaml:snakeyaml:1.17
|    +--- org.springframework.boot:spring-boot-starter-tomcat:1.5.2.RELEASE
|    |    +--- org.apache.tomcat.embed:tomcat-embed-core:8.5.11
|    |    +--- org.apache.tomcat.embed:tomcat-embed-el:8.5.11
|    |    \--- org.apache.tomcat.embed:tomcat-embed-websocket:8.5.11
|    |         \--- org.apache.tomcat.embed:tomcat-embed-core:8.5.11
|    +--- org.hibernate:hibernate-validator:5.3.4.Final
|    |    +--- javax.validation:validation-api:1.1.0.Final
|    |    +--- org.jboss.logging:jboss-logging:3.3.0.Final
|    |    \--- com.fasterxml:classmate:1.3.1 -> 1.3.3
|    +--- com.fasterxml.jackson.core:jackson-databind:2.8.7
|    |    +--- com.fasterxml.jackson.core:jackson-annotations:2.8.0
|    |    \--- com.fasterxml.jackson.core:jackson-core:2.8.7
|    +--- org.springframework:spring-web:4.3.7.RELEASE
|    |    +--- org.springframework:spring-aop:4.3.7.RELEASE (*)
|    |    +--- org.springframework:spring-beans:4.3.7.RELEASE (*)
|    |    +--- org.springframework:spring-context:4.3.7.RELEASE (*)
|    |    \--- org.springframework:spring-core:4.3.7.RELEASE
|    \--- org.springframework:spring-webmvc:4.3.7.RELEASE
|         +--- org.springframework:spring-aop:4.3.7.RELEASE (*)
|         +--- org.springframework:spring-beans:4.3.7.RELEASE (*)
|         +--- org.springframework:spring-context:4.3.7.RELEASE (*)
|         +--- org.springframework:spring-core:4.3.7.RELEASE
|         +--- org.springframework:spring-expression:4.3.7.RELEASE (*)
|         \--- org.springframework:spring-web:4.3.7.RELEASE (*)
+--- org.jetbrains.kotlin:kotlin-stdlib-jre8:1.1.1
|    \--- org.jetbrains.kotlin:kotlin-stdlib-jre7:1.1.1
|         \--- org.jetbrains.kotlin:kotlin-stdlib:1.1.1
|              \--- org.jetbrains:annotations:13.0
\--- org.jetbrains.kotlin:kotlin-reflect:1.1.1
     \--- org.jetbrains.kotlin:kotlin-stdlib:1.1.1 (*)

(*) - dependencies omitted (listed previously)

BUILD SUCCESSFUL

最新バージョンであればこちらでも確認できる。
http://docs.spring.io/spring-boot/docs/current/reference/htmlsingle/#appendix-dependency-versions

一応mavenリポジトリからも確認できる
https://repo1.maven.org/maven2/org/springframework/boot/spring-boot-dependencies/1.2.3.RELEASE/spring-boot-dependencies-1.2.3.RELEASE.pom

まあgradleが便利